Pith. sign in

REVIEW 2 major objections 6 minor 121 references

Reviewed by Pith at T0; open to challenge.

T0 means a machine referee read the full paper against a public rubric. The mark states how deep the mechanical check went, never who wrote it. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · glm-5.2

Radial flow in 3D gravity equals T̄T deformation — but isn't Hamiltonian

2026-07-09 23:53 UTC pith:M6675RSB

load-bearing objection Solid derivations within a narrow sector; the T̄T claim is overstated the 2 major comments →

arxiv 2607.06867 v1 pith:M6675RSB submitted 2026-07-07 hep-th gr-qc

On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity

Hamed Adami , Kristiansen Lara , Anouchah Latifi , Ren\'e Meyer This is my paper
classification hep-th gr-qc PACS 04.60.Kd11.25.Hf11.10.Ef
keywords Chern-Simons gravityT̄T deformationinverse scatteringbi-Hamiltonian hierarchyfinite-cutoff holographyBrown-York stress tensorKdV hierarchynon-compact boundary
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper studies three-dimensional Einstein gravity with negative cosmological constant on spatial boundaries that are non-compact (the real line rather than a circle), within the Chern-Simons gauge formulation. The authors restrict to a diagonal sector where the gauge connection lives along a single generator, reducing the boundary dynamics to two independent chiral transport equations. Within this sector, they derive an exact, closed-form expression for the quasi-local Brown-York stress tensor at any finite radial position — not just asymptotically. Differentiating this expression with respect to the radial coordinate yields a flow equation for the energy density whose right-hand side is the square root of the determinant of the stress tensor in an orthonormal frame. This is precisely the structure of a T̄T deformation, the solvable irrelevant deformation of two-dimensional field theories, here realized non-perturbatively and at arbitrary cutoff. The authors then develop the inverse-scattering description of the boundary dynamics. Because the spatial slice is non-compact, the boundary currents can be treated as potentials in a one-dimensional Schrödinger spectral problem, and the full nonlinear dynamics can be reconstructed via the Gelfand-Levitan-Marchenko equation. Soliton solutions correspond to reflectionless scattering data. The key finding at finite cutoff is that the quasi-local energy acquires a bilinear mixing term between left- and right-moving sectors that vanishes only at the asymptotic boundary. This term produces an effective interaction energy between left- and right-moving solitons that depends on their spatial overlap, even though the underlying chiral dynamics remain completely decoupled and integrable. Finally, the authors prove a no-go result: although the boundary time evolution is generated by a bi-Hamiltonian integrable hierarchy (the Gel'fand-Dikii / KdV hierarchy with central charge), the radial evolution cannot be cast as a Hamiltonian flow with respect to the same Poisson structure. The radial flow is exactly solvable but purely algebraic at each spatial point — it acts on the map between phase space variables and observables, not on the phase space itself.

Core claim

The central object is the exact radial flow equation for the quasi-local energy density, ∂ᵣρ = −4ℓ²r/(r⁴−ℓ⁴) √(ρ²−J²), where ρ is the energy density and J is the momentum density measured on a finite-radius hypersurface. This equation is derived in closed form from the Chern-Simons boundary data, holds at arbitrary radial cutoff rather than perturbatively near the boundary, and its right-hand side is the square root of the determinant of the stress tensor in an orthonormal frame — the invariant scalar that defines the T̄T deformation. The momentum density J is radially invariant. The equation is integrable by a linearizing substitution X = ρ + √(ρ²−J²), reducing to ∂ᵣ ln X = −4ℓ²r/(r⁴−ℓ⁴). A

What carries the argument

The paper combines four structures: (1) the Chern-Simons formulation of AdS₃ gravity with a diagonal reduction to abelian chiral sectors, giving exact algebraic expressions for the Brown-York stress tensor at finite radius; (2) the fluid/gravity correspondence interpreting the stress tensor as a conformal relativistic fluid with equation of state p = ρ; (3) the bi-Hamiltonian Gel'fand-Dikii hierarchy with two compatible Poisson structures — the first P± = ∂ₓ and the second D± = ∂ₓJ± + 2J±∂ₓ − (c±/24π)∂ₓ³, the classical Virasoro Poisson operator — generating infinitely many commuting Hamiltonians via the Lenard-Magri recursion; (4) the inverse-scattering transform for the Schrödinger operator

Load-bearing premise

All results hold within a restricted diagonal sector where the gauge connection is confined to a single generator, trivializing the nonlinear Chern-Simons term and reducing the dynamics to abelian chiral transport. Whether the T̄T flow equation, the bi-Hamiltonian structure, and the non-Hamiltonian radial flow conclusion survive in the full non-abelian phase space is not addressed.

What would settle it

The no-go theorem for Hamiltonian radial flow could be falsified by finding a local Hamiltonian functional on the boundary current algebra that reproduces the exact radial evolution — the paper claims no such functional exists within the canonical Poisson structure, but this is verified within the diagonal sector only. The T̄T flow equation itself could be falsified by checking that the exact Brown-York stress tensor, when differentiated radially, fails to satisfy ∂ᵣρ = −4ℓ²r/(r⁴−ℓ⁴) √(ρ²−J²) for some admissible boundary data — but the derivation is algebraic and exact within the stated ansatz

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The exact T̄T flow equation provides a non-perturbative radial evolution for quasi-local observables that resums all orders in the cutoff, going beyond the perturbative near-boundary expansions standard in holographic renormalization.
  • The no-go theorem for Hamiltonian radial flow distinguishes exact solvability from Hamiltonian integrability: the radial flow is solvable because it is algebraic, not because it is generated by a conserved charge, suggesting these are independent notions at finite cutoff.
  • The cutoff-induced soliton interaction energy, which depends on spatial overlap of left- and right-moving profiles, provides a geometric mechanism for effective interactions between sectors that remain dynamically decoupled — a purely observer-dependent effect with no dynamical force.
  • The spectral data (reflection coefficients, discrete eigenvalues, norming constants) of the inverse-scattering formulation acquire direct gravitational meaning as observables parametrizing the boundary phase space, with discrete eigenvalues labeling solitonic boundary excitations of locally AdS₃ geometries.
  • The framework applies to non-compact spatial slices where inverse scattering is available, complementing the compact case where Floquet theory and finite-gap solutions replace the Jost-function formalism.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the diagonal sector restriction were lifted, the nonlinear term a∧a in the Chern-Simons connection would no longer vanish, and the chiral sectors would couple dynamically. Whether the T̄T flow equation survives in modified form or is replaced by a more complex radial evolution is the natural next question — the no-go theorem for Hamiltonian radial flow might also fail or require modification in
  • The distinction between solvability and Hamiltonian integrability of the radial flow could be a general feature of finite-cutoff holography beyond three dimensions: in higher dimensions where the bulk has local degrees of freedom, the radial flow is no longer purely algebraic, but the conceptual gap between radial evolution and boundary Hamiltonian structure may persist.
  • The anisotropic Lifshitz scaling symmetry of the hierarchy, where each Hamiltonian flow has its own dynamical exponent 2I+1, suggests a potential connection to higher-spin holography where different spin fields naturally carry different scaling weights — the hierarchy of commuting charges might organize according to spin content in a higher-spin extension.
  • The appearance of islands and replica wormholes requires open boundary conditions, which may be incompatible with the falloff conditions needed for inverse scattering. Investigating whether a modified spectral framework accommodates open boundaries could connect integrable boundary dynamics to the information paradox in three-dimensional gravity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This manuscript studies three-dimensional Einstein gravity with negative cosmological constant on non-compact spatial boundaries within the Chern-Simons formulation. Working in a diagonal sector where the gauge connection is restricted to the Cartan generator L_0, the authors derive an exact closed-form expression for the quasi-local Brown-York stress tensor at arbitrary radial position. From this, they obtain a radial flow equation for the energy density and discuss its relation to the holographic T T̄ deformation. They further develop the inverse-scattering description of the boundary dynamics, identify the gravitational interpretation of spectral data, analyze soliton solutions and their finite-cutoff deformation, and prove a no-go theorem showing that the radial flow is not Hamiltonian with respect to the canonical Poisson structure of the boundary currents. The paper unifies integrability, quasi-local observables, inverse scattering, and finite-cutoff holography in a single framework.

Significance. The paper makes several contributions of interest to the holography and integrable systems communities. The derivation of an exact, non-perturbative radial flow equation (Eq. 63) from the closed-form Brown-York stress tensor is a concrete result that goes beyond the usual near-boundary FG expansion. The identification of spectral data (reflection coefficients, bound-state eigenvalues, norming constants) with gravitational observables on non-compact boundaries is a natural but valuable observation that connects inverse scattering to the gravitational phase space. The no-go theorem for a Hamiltonian description of the radial flow is clean and correct within the diagonal sector: since J_± are r-independent by construction, no Hamiltonian vector field on the canonical phase space can generate radial evolution. The soliton solutions and the analysis of the cutoff-induced interaction energy (Eq. 121) are explicit and illustrative. The framework is parameter-free in the sense that the radial flow follows algebraically from the exact stress tensor without fitted constants.

major comments (2)
  1. The abstract states that the radial flow equation 'realizes the holographic T T̄ deformation at finite cutoff,' and the introduction (Sec. I) describes it as providing 'a direct gravitational realization of the finite-cutoff flow.' However, Eq. (63) involves sqrt(rho^2 - J^2) = sqrt(det T), whereas the standard T T̄ flow is governed by det T = rho^2 - J^2 (quadratic in the stress tensor components). For J=0, Eq. (63) reduces to a linear ODE in rho, while the standard T T̄ flow gives a quadratic ODE. No reparametrization of the radial coordinate can convert a linear ODE into a quadratic one. The authors acknowledge in Sec. VII that the result 'does not establish an exact equivalence with the universal T T̄ flow,' but this qualification is absent from the abstract and introduction. The language should be tempered to accurately reflect the structural relationship: the flow is T T̄-like in涉及
  2. All results are derived within the diagonal sector (Eq. 13), where the gauge connection is restricted to the Cartan generator L_0. This trivializes the nonlinear term a∧a and reduces the dynamics to abelian chiral transport equations. The bi-Hamiltonian structure (Eq. 76), the Lax pair (Eq. 91), the radial flow (Eq. 63), and the no-go theorem all hold only within this reduced sector. The paper does not address whether any of these results survive in the full non-abelian phase space. While sector restrictions are common in the literature, the scope should be stated more prominently, especially in the abstract and introduction, so readers understand the precise domain of validity.
minor comments (6)
  1. Sec. VII, Eq. (63): The statement that the quantity under the square root is 'identically a perfect square for arbitrary J_± throughout the physical region r > ℓ' could benefit from an explicit demonstration, as it is important for the reality of the flow.
  2. Sec. IX, Eq. (76): The second Hamiltonian structure D_± is identified as the classical Virasoro Poisson operator. The relationship between the central charge c_± appearing here and the Brown-Henneaux central charge should be clarified for the reader.
  3. Sec. X.B, Eq. (108): The soliton profile J_± = -ν_± α_±^2 sech^2(α_± ξ_±) is standard, but the gravitational interpretation as a boundary excitation of locally AdS3 spacetime could be stated more sharply — in particular, the relation to the Bañados family and the role of boundary diffeomorphisms.
  4. Sec. XI, Eq. (119a): The decomposition of quasi-local energy into E_∞ and E_int is clear, but the statement that 'the finite-cutoff theory does not couple the chiral sectors dynamically' could be contrasted more explicitly with what a genuine dynamical coupling would look like.
  5. The reference list is extensive but several citations in the introduction (e.g., to the T T̄ literature) could be more precisely matched to specific claims.
  6. Sec. XII.D, Eq. (124): The reduction to the linear ODE via X = ρ + sqrt(ρ^2 - J^2) is elegant; including one line of algebra showing the substitution would help the reader verify the claim.

Circularity Check

0 steps flagged

No significant circularity: the radial flow equation is a parameter-free algebraic consequence of the exact Brown–York stress tensor, and self-citations are contextual rather than load-bearing.

full rationale

The paper's central derivation chain is self-contained. The Chern–Simons formulation and diagonal reduction (Eq. 13) restrict to a sector but do not define outputs in terms of themselves. The exact Brown–York stress tensor (Eqs. 57a–57b) is computed directly from the reconstructed bulk metric (Eq. 37) via the standard fluid/gravity dictionary. The radial flow equation (Eq. 63) is then obtained by differentiating ρ with respect to r at fixed J± and algebraically eliminating J± in favor of (ρ, J)—a legitimate, non-circular manipulation of two equations in two unknowns. No fitted parameters appear anywhere. The bi-Hamiltonian hierarchy (Sec. IX) uses the standard Gel'fand–Dikii/Magri construction, which is external mathematical machinery. The no-go theorem (Sec. XII.D) follows from the observation that J± are r-independent by construction in radial gauge, so radial evolution cannot be a Hamiltonian flow on the J± phase space—this is a logical argument, not a self-referential one. Self-citation [31] (Adami & Latifi) provides prior context for inverse scattering on non-compact boundaries but is not load-bearing for the radial flow equation, the T̄T identification, or the no-go theorem. The skeptic's concern that the flow involves √(det T) rather than det(T), making it structurally distinct from the standard T̄T flow, is a correctness/overstatement issue rather than a circularity one—the paper itself acknowledges (Sec. VII) that the result 'does not establish an exact equivalence with the universal T̄T flow.' The abstract's stronger language is an overstatement of scope, not a circular derivation. Score 1 reflects the minor contextual self-citation without load-bearing circularity in the central results.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

No new physical entities are postulated. The framework uses established mathematical structures (Chern–Simons connections, Schrödinger operators, GLM kernels) applied to gravitational boundary data. The 'effective interaction energy' E_int (Eq. 121) is a derived observable, not a new entity.

free parameters (2)
  • ν± (Lax operator normalization) = c±/(6π)
    Fixed by consistency of the soliton reconstruction with the hierarchy evolution (Eq. 114). Not fitted to data but determined by matching two independent calculations.
  • c± (central charge) = not specified numerically
    Enters the second Poisson structure (Eq. 76) and Hamiltonians. Treated as an input parameter from the gravitational theory (k = ℓ/4G), not fitted within this paper.
axioms (4)
  • domain assumption Diagonal reduction: gauge connections take values along L₀ only (Eq. 13)
    Restricts to a subsector where a∧a = 0. Invoked in Sec. II to reduce field equations to abelian chiral transport. All results depend on this restriction.
  • domain assumption Short-range falloff of J±(t,x) at spatial infinity
    Required for inverse scattering (Jost solutions, GLM equation). Stated in Sec. X.A. Natural for non-compact boundaries but excludes certain physical configurations.
  • domain assumption Vanishing symplectic flux through the asymptotic boundary (Eq. 67)
    Required for Hamiltonian formulation of boundary dynamics (Sec. VIII). Standard in AdS₃ holography but a genuine assumption about boundary conditions.
  • standard math Compatibility of Poisson structures P± and D± (Schouten bracket vanishes)
    Standard Gel'fand–Dikii structure; invoked in Sec. IX. Well-established in integrable systems literature.

pith-pipeline@v1.1.0-glm · 37946 in / 2682 out tokens · 299501 ms · 2026-07-09T23:53:41.225743+00:00 · methodology

0 comments
read the original abstract

We study three-dimensional Einstein gravity with negative cosmological constant on non-compact spatial boundaries within the Chern-Simons formulation. Using an exact fluid/gravity correspondence, we derive a closed radial flow equation for the quasi-local stress tensor and show that it realizes the holographic $T\bar T$ deformation at finite cutoff. We further develop the inverse-scattering description of the boundary dynamics, identifying the gravitational interpretation of the associated spectral data and analyzing the finite-cutoff deformation of soliton solutions. Although the boundary evolution is governed by an integrable bi-Hamiltonian hierarchy, we show that the radial flow itself is not Hamiltonian with respect to the canonical Poisson structure. Our results establish a unified framework connecting integrability, quasi-local gravitational observables, inverse scattering, and finite-cutoff holography on non-compact boundaries.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

121 extracted references · 121 canonical work pages · 91 internal anchors

  1. [1]

    Af- ter a suitable rescaling of the coordinateξ±, it reduces to the Pöschl–Teller potential with parameterl= 1, a prototypical reflectionless system

    Spectral problem For the single–soliton configuration (108), the Schrödinger equation (89) becomes exactly solvable. Af- ter a suitable rescaling of the coordinateξ±, it reduces to the Pöschl–Teller potential with parameterl= 1, a prototypical reflectionless system. In this case, the spectral problem exhibits a sim- ple structure: there is a single bound ...

    work page

  2. [2]

    Fixing the time evolution The dynamics of the hierarchy is determined by the bi- Hamiltonian structure (75). Choosing the Hamiltonian associated with the(I+ 1)-th flow fixes the chemical po- tentials to be µ± =R I+1[J±].(112) Combining (20) with (109) then yields the evolution equation ∓ π k J± ∂tf± ±∂ tφ± =R I+1[J±].(113) For generic flows withI≥0, consi...

    work page

  3. [3]

    T¯T-deformed Gel’fand–Dikii hierarchy

    Hamiltonians The Lifshitz scaling symmetry also determines the functional dependence of the conserved Hamiltonians on the soliton parameters. In the single-soliton sector, the parameterα ± istheonlyindependentdimensionfulquan- tity. Consequently, homogeneity under (85) requires the Hamiltonian generating the(I+ 1)-th flow to scale as H ± I+1 ∝α 2I+3 ± . T...

    work page

  4. [4]

    Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,

    J. D. Brown and M. Henneaux, “Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,” Commun. Math. Phys.104(1986) 207–226

    work page 1986

  5. [5]

    Asymptotically anti-De Sitter Spaces,

    M. Henneaux and C. Teitelboim, “Asymptotically anti-De Sitter Spaces,”Commun. Math. Phys.98 (1985) 391–424

    work page 1985

  6. [6]

    (2+1)-dimensional gravity as an exactly soluble system,

    E. Witten, “(2+1)-dimensional gravity as an exactly soluble system,”Nucl. Phys.B311(1988) 46

    work page 1988

  7. [7]

    Carlip,Quantum gravity in 2+1 dimensions

    S. Carlip,Quantum gravity in 2+1 dimensions. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 12, 2003

    work page 2003

  8. [8]

    Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole

    S. Carlip, “Conformal field theory, (2+1)-dimensional gravity, and the BTZ black hole,”Class. Quant. Grav. 22(2005) R85–R124,gr-qc/0503022

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  9. [9]

    The Black Hole in Three Dimensional Space Time

    M. Banados, C. Teitelboim, and J. Zanelli, “The Black hole in three-dimensional space-time,”Phys. Rev. Lett. 69(1992) 1849–1851,hep-th/9204099

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  10. [10]

    Dimensionally Continued Black Holes

    M. Banados, C. Teitelboim, and J. Zanelli, “Dimensionally continued black holes,”Phys. Rev. D 49(1994) 975–986,gr-qc/9307033

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  11. [11]

    A Chern-Simons action for three-dimensional Anti-de Sitter supergravity theories,

    A. Achucarro and P. K. Townsend, “A Chern-Simons action for three-dimensional Anti-de Sitter supergravity theories,”Phys. Lett.B180(1986) 89

    work page 1986

  12. [12]

    Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory,

    S. Elitzur, G. W. Moore, A. Schwimmer, and N. Seiberg, “Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory,”Nucl. Phys. B326(1989) 108–134

    work page 1989

  13. [13]

    The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant

    O. Coussaert, M. Henneaux, and P. van Driel, “The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant,” Class.Quant.Grav.12(1995) 2961–2966, gr-qc/9506019

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  14. [14]

    Global Charges in Chern-Simons theory and the 2+1 black hole

    M. Bañados, “Global charges in Chern-Simons field theory and the (2+1) black hole,”Phys. Rev.D52 (1995) 5816,hep-th/9405171

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  15. [15]

    Three-dimensional quantum geometry and black holes

    M. Bañados, “Three-dimensional quantum geometry and black holes,”hep-th/9901148

    work page internal anchor Pith review Pith/arXiv arXiv

  16. [16]

    Advanced Lectures on General Relativity

    G. Compère and A. Fiorucci, “Advanced Lectures on General Relativity,”Lect. Notes Phys.952(2019) 150, 1801.07064

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  17. [17]

    Boundary conditions for General Relativity on AdS$_{3}$ and the KdV hierarchy

    A. Pérez, D. Tempo, and R. Troncoso, “Boundary conditions for General Relativity on AdS3 and the KdV hierarchy,”JHEP06(2016) 103,1605.04490

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  18. [18]

    Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies

    E. Ojeda and A. Pérez, “Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies,” JHEP08(2019) 079,1906.11226

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  19. [19]

    Integrable systems and the boundary dynamics of higher spin gravity on AdS$_3$

    E. Ojeda and A. Pérez, “Integrable systems and the boundary dynamics of higher spin gravity on AdS3,” JHEP11(2020) 089,2009.07829

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  20. [20]

    Revisiting the asymptotic dynamics of General Relativity on AdS$_3$

    H. A. González, J. Matulich, M. Pino, and R. Troncoso, “Revisiting the asymptotic dynamics of General Relativity on AdS3,”JHEP12(2018) 115, 1809.02749

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  21. [21]

    Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

    A. Campoleoni, S. Fredenhagen, S. Pfenninger, and S. Theisen, “Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields,”JHEP1011(2010) 007,1008.4744

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  22. [22]

    Asymptotic W-symmetries in three-dimensional higher-spin gauge theories

    A. Campoleoni, S. Fredenhagen, and S. Pfenninger, “Asymptotic W-symmetries in three-dimensional higher-spin gauge theories,”JHEP1109(2011) 113, 1107.0290

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  23. [23]

    Integrable Systems and Spacetime Dynamics

    M. Cárdenas, F. Correa, K. Lara, and M. Pino, “Integrable Systems and Spacetime Dynamics,”Phys. Rev. Lett.127(2021), no. 16, 161601,2104.09676

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  24. [24]

    Integrable black hole dynamics in the asymptotic structure of AdS$_{3}$

    M. Cárdenas, F. Correa, and M. Pino, “Integrable black hole dynamics in the asymptotic structure of AdS3,”2504.20292

    work page internal anchor Pith review Pith/arXiv arXiv

  25. [25]

    1/c deformations of AdS$_3$ boundary conditions and the Dym hierarchy

    K. Lara, M. Pino, and F. Reyes, “1/c deformations of AdS3 boundary conditions and the Dym hierarchy,” JHEP11(2024) 042,2401.12338

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  26. [26]

    Non-axisymmetric (2+1) black holes with Dym boundary conditions,

    M. Pino and F. Reyes, “Non-axisymmetric (2+1) black holes with Dym boundary conditions,”2511.06567

    work page arXiv

  27. [27]

    W Symmetry and Integrability of Higher spin black holes

    G. Compère and W. Song, “Wsymmetry and integrability of higher spin black holes,”JHEP1309 (2013) 144,1306.0014

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  28. [28]

    Generalized Fefferman-Graham gauge and boundary Weyl structures

    G. Arenas-Henriquez, F. Diaz, and D. Rivera-Betancour, “Generalized Fefferman-Graham gauge and boundary Weyl structures,”JHEP02 (2025) 007,2411.12513

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  29. [29]

    Integrable systems with BMS$_{3}$ Poisson structure and the dynamics of locally flat spacetimes

    O. Fuentealba, J. Matulich, A. Pérez, M. Pino, P. Rodríguez, D. Tempo, and R. Troncoso, “Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes,”JHEP01(2018) 148,1711.02646

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  30. [30]

    Soft Heisenberg hair on black holes in three dimensions

    H. Afshar, S. Detournay, D. Grumiller, W. Merbis, A. Perez, D. Tempo, and R. Troncoso, “Soft Heisenberg hair on black holes in three dimensions,” Phys. Rev.D93(2016), no. 10, 101503,1603.04824

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  31. [31]

    Near horizon dynamics of three dimensional black holes

    D. Grumiller and W. Merbis, “Near horizon dynamics of three dimensional black holes,”SciPost Phys.8 (2020), no. 1, 010,1906.10694

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  32. [32]

    BTZ black hole with KdV-type boundary conditions: Thermodynamics revisited

    C. Erices, M. Riquelme, and P. Rodríguez, “BTZ black hole with Korteweg–de Vries-type boundary conditions: Thermodynamics revisited,”Phys. Rev. D 100(2019), no. 12, 126026,1907.13026

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  33. [33]

    KdV-charged black holes

    A. Dymarsky and S. Sugishita, “KdV-charged black holes,”JHEP05(2020) 041,2002.08368

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  34. [34]

    Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows

    H. Adami and A. Latifi, “Integrability in Three-Dimensional Gravity: Eigenfunction-Forced KdV Flows,”2510.10519

    work page internal anchor Pith review Pith/arXiv arXiv

  35. [35]

    On the Holographic Renormalization Group

    J. de Boer, E. P. Verlinde, and H. L. Verlinde, “On the holographic renormalization group,”JHEP08(2000) 003,hep-th/9912012

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  36. [36]

    Holographic Renormalization

    M. Bianchi, D. Z. Freedman, and K. Skenderis, “Holographic Renormalization,”Nucl. Phys.B631 (2002) 159–194,hep-th/0112119

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  37. [37]

    Lecture Notes on Holographic Renormalization

    K. Skenderis, “Lecture notes on holographic renormalization,”Class. Quant. Grav.19(2002) 5849–5876,hep-th/0209067

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  38. [38]

    AdS/CFT correspondence and Geometry

    I. Papadimitriou and K. Skenderis, “AdS / CFT correspondence and geometry,”IRMA Lect. Math. Theor. Phys.8(2005) 73–101,hep-th/0404176

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  39. [39]

    Holographic and Wilsonian Renormalization Groups

    I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,”JHEP06(2011) 031,1010.1264

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  40. [40]

    Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm

    T. Faulkner, H. Liu, and M. Rangamani, “Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm,”JHEP08(2011) 051, 1010.4036

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  41. [41]

    Gravity Is Induced By Renormalization Group Flow

    H. Adami, M. M. Sheikh-Jabbari, and V. Taghiloo, “Gravity Is Induced By Renormalization Group Flow,” 2508.09633

    work page internal anchor Pith review Pith/arXiv arXiv

  42. [42]

    Moving the CFT into the bulk with $T\bar T$

    L. McGough, M. Mezei, and H. Verlinde, “Moving the CFT into the bulk withTT,”JHEP04(2018) 010, 1611.03470. 24

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  43. [43]

    Expectation value of composite field $T{\bar T}$ in two-dimensional quantum field theory

    A. B. Zamolodchikov, “Expectation value of composite field T anti-T in two-dimensional quantum field theory,”hep-th/0401146

    work page internal anchor Pith review Pith/arXiv arXiv

  44. [44]

    On space of integrable quantum field theories

    F. A. Smirnov and A. B. Zamolodchikov, “On space of integrable quantum field theories,”Nucl. Phys. B915 (2017) 363–383,1608.05499

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  45. [45]

    $T \bar{T}$-deformed 2D Quantum Field Theories

    A. Cavaglià, S. Negro, I. M. Szécsényi, and R. Tateo, “T¯T-deformed 2D Quantum Field Theories,”JHEP10 (2016) 112,1608.05534

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  46. [46]

    Holography at finite cutoff with a $T^2$ deformation

    T. Hartman, J. Kruthoff, E. Shaghoulian, and A. Tajdini, “Holography at finite cutoff with aT2 deformation,”JHEP03(2019) 004,1807.11401

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  47. [47]

    Modular invariance and uniqueness of $T\bar{T}$ deformed CFT

    O. Aharony, S. Datta, A. Giveon, Y. Jiang, and D. Kutasov, “Modular invariance and uniqueness of T ¯Tdeformed CFT,”JHEP01(2019) 086,1808.02492

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  48. [48]

    TT deformations in general dimensions

    M. Taylor, “T¯Tdeformations in general dimensions,” Adv. Theor. Math. Phys.27(2023), no. 1, 37–63, 1805.10287

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  49. [49]

    Cutoff AdS$_3$ versus the $T\bar{T}$ deformation

    P. Kraus, J. Liu, and D. Marolf, “Cutoff AdS3 versus theT Tdeformation,”JHEP07(2018) 027, 1801.02714

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  50. [50]

    $T\bar T$ and the mirage of a bulk cutoff

    M. Guica and R. Monten, “T¯Tand the mirage of a bulk cutoff,”SciPost Phys.10(2021), no. 2, 024, 1906.11251

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  51. [51]

    An integrable Lorentz-breaking deformation of two-dimensional CFTs

    M. Guica, “An integrable Lorentz-breaking deformation of two-dimensional CFTs,”SciPost Phys. 5(2018), no. 5, 048,1710.08415

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  52. [52]

    $J\bar{T}$ deformed $CFT_2$ and String Theory

    S. Chakraborty, A. Giveon, and D. Kutasov, “JT deformed CFT2 and string theory,”JHEP10(2018) 057,1806.09667

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  53. [53]

    Strings on warped AdS$_3$ via $T\bar{J}$ deformations

    L. Apolo and W. Song, “Strings on warped AdS3 via T¯Jdeformations,”JHEP10(2018) 165,1806.10127

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  54. [54]

    Local Fluid Dynamical Entropy from Gravity

    S. Bhattacharyya, V. E. Hubeny, R. Loganayagam, G. Mandal, S. Minwalla, T. Morita, M. Rangamani, and H. S. Reall, “Local Fluid Dynamical Entropy from Gravity,”JHEP06(2008) 055,0803.2526

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  55. [55]

    Forced Fluid Dynamics from Gravity

    S. Bhattacharyya, R. Loganayagam, S. Minwalla, S. Nampuri, S. P. Trivedi, and S. R. Wadia, “Forced Fluid Dynamics from Gravity,”JHEP02(2009) 018, 0806.0006

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  56. [56]

    Fluid dynamics of R-charged black holes

    J. Erdmenger, M. Haack, M. Kaminski, and A. Yarom, “Fluid dynamics of R-charged black holes,”JHEP01 (2009) 055,0809.2488

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  57. [57]

    Hydrodynamics from charged black branes

    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam, and P. Surowka, “Hydrodynamics from charged black branes,”JHEP 01(2011) 094,0809.2596

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  58. [58]

    Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence

    M. Rangamani, “Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence,”Class. Quant. Grav.26(2009) 224003,0905.4352

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  59. [59]

    The fluid/gravity correspondence,

    V. E. Hubeny, S. Minwalla, and M. Rangamani, “The fluid/gravity correspondence,” inTheoretical Advanced Study Institute in Elementary Particle Physics: String theory and its Applications: From meV to the Planck Scale, pp. 348–383. 2012.1107.5780

    work page arXiv 2012

  60. [60]

    Most general AdS_3 boundary conditions

    D. Grumiller and M. Riegler, “Most general AdS3 boundary conditions,”JHEP10(2016) 023, 1608.01308

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  61. [61]

    Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes

    H. Afshar, D. Grumiller, and M. M. Sheikh-Jabbari, “Near horizon soft hair as microstates of three dimensional black holes,”Phys. Rev.D96(2017), no. 8, 084032,1607.00009

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  62. [62]

    Role of surface integrals in the Hamiltonian formulation of general relativity,

    T. Regge and C. Teitelboim, “Role of surface integrals in the Hamiltonian formulation of general relativity,” Ann. Phys.88(1974) 286

    work page 1974

  63. [63]

    Covariant theory of asymptotic symmetries, conservation laws and central charges

    G. Barnich and F. Brandt, “Covariant theory of asymptotic symmetries, conservation laws and central charges,”Nucl. Phys.B633(2002) 3–82, hep-th/0111246

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  64. [64]

    Local symmetries and constraints,

    J. Lee and R. M. Wald, “Local symmetries and constraints,”J. Math. Phys.31(1990) 725–743

    work page 1990

  65. [65]

    Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy

    V. Iyer and R. M. Wald, “Some properties of Nöther charge and a proposal for dynamical black hole entropy,”Phys. Rev.D50(1994) 846–864, gr-qc/9403028

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  66. [66]

    A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity

    R. M. Wald and A. Zoupas, “A General definition of ’conserved quantities’ in general relativity and other theories of gravity,”Phys.Rev.D61(2000) 084027, gr-qc/9911095

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  67. [67]

    Quasilocal energy and conserved charges derived from the gravitational action,

    J. D. Brown and J. W. York, Jr., “Quasilocal energy and conserved charges derived from the gravitational action,”Phys. Rev.D47(1993) 1407–1419

    work page 1993

  68. [68]

    A Stress Tensor for Anti-de Sitter Gravity

    V. Balasubramanian and P. Kraus, “A stress tensor for anti-de Sitter gravity,”Commun. Math. Phys.208 (1999) 413–428,hep-th/9902121

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  69. [69]

    Black Hole Entropy from Near-Horizon Microstates

    A. Strominger, “Black hole entropy from near-horizon microstates,”JHEP02(1998) 009,hep-th/9712251

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  70. [70]

    The Large N Limit of Superconformal Field Theories and Supergravity

    J. M. Maldacena, “The largeNlimit of superconformal field theories and supergravity,”Adv. Theor. Math. Phys.2(1998) 231–252,hep-th/9711200

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  71. [71]

    Anti De Sitter Space And Holography

    E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys.2(1998) 253–291, hep-th/9802150

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  72. [72]

    Gauge Theory Correlators from Non-Critical String Theory

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,”Phys. Lett.B428(1998) 105–114, hep-th/9802109

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  73. [73]

    Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations

    H. Babaei-Aghbolagh, K. B. Velni, D. M. Yekta, and H. Mohammadzadeh, “Emergence of non-linear electrodynamic theories from TT¯-like deformations,” Phys. Lett. B829(2022) 137079,2202.11156

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  74. [74]

    Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions

    H. Babaei-Aghbolagh, K. Babaei Velni, D. Mahdavian Yekta, and H. Mohammadzadeh, “Marginal TT¯-like deformation and modified Maxwell theories in two dimensions,”Phys. Rev. D 106(2022), no. 8, 086022,2206.12677

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  75. [75]

    Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions

    R. Conti, J. Romano, and R. Tateo, “Metric approach to aT T-like deformation in arbitrary dimensions,” JHEP09(2022) 085,2206.03415

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  76. [76]

    Root-$T \overline{T}$ Deformations in Two-Dimensional Quantum Field Theories

    C. Ferko, A. Sfondrini, L. Smith, and G. Tartaglino-Mazzucchelli, “Root-T¯TDeformations in Two-Dimensional Quantum Field Theories,”Phys. Rev. Lett.129(2022), no. 20, 201604,2206.10515

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  77. [77]

    Root-$T \overline{T}$ Deformed Boundary Conditions in Holography

    S. Ebert, C. Ferko, and Z. Sun, “Root-TT¯deformed boundary conditions in holography,”Phys. Rev. D107 (2023), no. 12, 126022,2304.08723

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  78. [78]

    Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations

    D. Tempo and R. Troncoso, “Nonlinear automorphism of the conformal algebra in 2D and continuous √ T T deformations,”JHEP12(2022) 129,2210.00059

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  79. [79]

    Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations

    P. Rodríguez, D. Tempo, and R. Troncoso, “Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite √ T Tdeformations,” JHEP11(2021) 133,2106.09750

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  80. [80]

    On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT

    A. Banerjee, P. Parekh, and R. Raj, “On √ T T deformed pathways: CFT to CCFT,”JHEP05(2026) 267,2601.15376. 25

    work page internal anchor Pith review Pith/arXiv arXiv 2026

Showing first 80 references.