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A single linearised massive p-form determines the low-energy thermal spectrum of an entire family of holographic theories with exact or weakly broken higher-form symmetries.

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2026-08-04 13:30 UTC pith:V4EEVKLQ

load-bearing objection Solid, internally consistent p-form generalisation of the holographic quasihydrodynamics dictionary; the single-field truncation is an asserted EFT minimality assumption rather than a proven reduction, so treat the exhaustive-spectrum claim as conditional. the 3 major comments →

arxiv 2509.26583 v3 pith:V4EEVKLQ submitted 2025-09-30 hep-th cond-mat.str-elgr-qc

Higher-form (Quasi)Hydrodynamics from Holography: Deformations and Dualities

Andr\'e Oliveira Pinheiro This is my paper
classification hep-th cond-mat.str-elgr-qc
keywords higher-form symmetriesquasihydrodynamicsholographydouble-trace deformationsStückelberg p-formHodge dualityemergent photonsthermal correlators
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 tries to establish that a one-parameter family of holographic theories — massless and slightly massive p-form fields in anti-de Sitter space with double-trace boundary deformations — has a completely solvable low-energy sector. If the central claim is right, the thermal response of any such system is known analytically: exact higher-form symmetries give diffusion at weak deformation and emergent photons at strong deformation, while weakly broken symmetries give a triad of slow relaxation regimes connected by pole collisions and Hodge-type dualities. The value would be a controlled template for quasihydrodynamics beyond the standard hydrodynamic expansion, including the effect of defects and charged operators that break the symmetry. The paper also argues that in the low-density limit, stable diffusion of sufficiently high-dimensional charged objects requires relevant double-trace deformations.

Core claim

The paper claims that the low-energy spectrum of boundary systems with exact or approximate higher-form charges is determined, across the whole theory space, by the bulk mass and a single double-trace coupling. For massless p-forms, weak double-trace deformations yield a hydrodynamic diffusion pole; as the deformation grows, a second slowly relaxing pole enters and collides with it, producing a pair of attenuated sound modes that become undamped photons in the infinite-deformation limit. For massive p-forms, the same coupling plus a small bulk mass produces a triad of quasihydrodynamic regimes with pole collisions, and the spectra are constrained by electric-magnetic Hodge duality (λ→4−λ), m

What carries the argument

The load-bearing object is the Higher Stückelberg action: a bulk action for a massive (n+1)-form field built from gauge-invariant combinations H=dB and F proportional to d(A/θ)+B. This is the linearised realisation of the defect/charged-operator picture of Section 2.3.3. Combined with Robin boundary conditions that implement double-trace deformations, holographic renormalisation via 'counterterms+' establishes the dictionary; the Hodge star maps between Maxwell equations of different rank (electric-magnetic duality) and the massive analogue λ→6−λ; and ingoing boundary conditions at the black-brane horizon convert the bulk equations into closed hydrodynamic and quasihydrodynamic equations for

Load-bearing premise

Everything rests on the assumption that a single linearised massive p-form (the Higher Stückelberg action) captures all leading low-energy dynamics of a boundary system with one weakly broken higher-form symmetry; if other light bulk modes or nonlinear defect couplings contribute at order k∼m≪T, the predicted mode triad, pole collisions, and dualities would not describe the real system.

What would settle it

Compute the retarded current-current correlator in a boundary lattice model or in a holographic theory with explicit defect fields beyond the Stückelberg action, and look at the second-lowest pole at k∼m; the paper predicts a specific pole collision and subsequent relaxation/sound transition as the deformation magnitude grows. If the pole either does not appear or collides at a different deformation scale, the linearised Stückelberg model is insufficient.

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

If this is right

  • For any dimension d, form rank, quantisation scheme, and deformation scale, the low-lying poles of thermal correlators are known analytically in the k∼m≪T regime (excluding the singular case λ=3).
  • Strong double-trace deformation turns a diffusive mode into a pair of attenuated sound modes that become lossless, light-speed photons in the massless limit.
  • Massive theories display a relaxation-mode triad with two pole collisions, and the spectra of dual theories are related by Hodge dualities, so knowing one spectrum determines its duals.
  • The massless correlators arise as a zero-mass limit of the massive ones, with the limiting matrices degenerate — signalling an emergent gauge symmetry that protects propagation.
  • In the low-density limit, stable diffusion of sufficiently high-dimensional charged objects requires relevant deformations; otherwise the modes are unstable.

Where Pith is reading between the lines

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

  • Editorial inference: the pole-collision structure suggests a universal 'mode-merging' mechanism — when a gapped relaxation mode enters the low-energy window, it collides with the diffusive mode and converts into propagating sound. This could be tested in lattice or cold-atom realisations of higher-form symmetries by tuning the deformation strength.
  • Editorial inference: the strong/weak duality M+ M− = 1 hints that the deformed boundary theories sit on a conformal manifold with an exact S-duality; a natural extension is to search for self-dual points, especially at λ=3 and at the self-dual line λ=2, where the paper leaves constraints open.
  • Editorial inference: the linearised Stückelberg truncation is the only step where additional bulk fields are neglected; if nonlinear defect dynamics or additional light modes contribute at leading order in k∼m≪T, the predicted triad structure and duality maps would be modified, providing a clean diagnostic of the truncation's validity.

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

3 major / 5 minor

Summary. The paper develops a holographic framework for systems with exact and approximate continuous higher-form symmetries, using massless and massive p-form fields in asymptotically AdS spacetimes. It implements double-trace deformations through Robin boundary conditions, performs holographic renormalisation for both electric and magnetic quantisation, and derives bulk Hodge-type dualities and their boundary consequences. At finite temperature, the author computes retarded thermal two-point functions in the hydrodynamic limit k ~ m << T for both massless and massive theories, and extracts spectra that include diffusion, relaxation, pole collisions, attenuated sound, and emergent photons. The paper claims to determine the low-energy spectrum for the entire theory space, excluding λ=3.

Significance. The paper is technically substantial and ambitious. If the results are correct, they provide a unified analytic characterisation of holographic higher-form hydrodynamics and quasihydrodynamics over a wide family of theories, generalising earlier work by Grozdanov, Lucas, Poovuttikul and others to arbitrary ranks, masses, and double-trace deformations. The strengths include the systematic holographic dictionary, explicit correlator computations, the massless limit as a consistency check, and the explicit duality maps between quantisation schemes. The author is also candid about several limitations, such as the exclusion of λ=3, the restriction to |m^2|<<1, and the fact that holographic renormalisation is only performed to leading order for large |λ̄−2| and |λ−3|. However, the completeness of the single-p-form truncation and the scheme dependence of O(k^2) data in the unrenormalised ranges are structural gaps that need to be addressed before the full claims can be accepted.

major comments (3)
  1. [Sections 2.3.3 and 3.1, Eq. (3.8)] The reduction of the two-field defect/charged-operator action to the Higher Stückelberg action is obtained by a field redefinition and by dropping all nonlinear terms. The paper does not prove that no other light bulk mode of the parent theory couples at order k~m<<T. For a concrete parent such as an Abelian-Higgs model, a dynamical radial mode with mass comparable to or smaller than m would contribute additional slow degrees of freedom and would alter the spectra in Eqs. (6.50)-(6.56) and the duality maps. The text asserts this as an EFT minimality assumption rather than deriving it from a class of UV completions. Since the headline claim is the exhaustive low-energy spectrum for the entire theory space, this truncation is load-bearing. Please either exhibit a class of embeddings in which decoupling is guaranteed, or state explicitly the mass/regime conditions under which the single-p-f
  2. [Sections 4.1, 4.2 and 7] Holographic renormalisation is completed only for 0≤λ̄≤4 in the massless case and for 2≤λ≤4 (or 1≤λ≤5 for m^2<0) in the massive case. For other values of λ̄ and λ, the O(□) terms in the on-shell action contain uncancelled divergences, and the renormalised variables (4.11) are defined only up to unspecified O(□) counterterms. Since the hydrodynamic diffusion constant is the O(k^2) coefficient of the retarded correlator, these ambiguities can shift the pole locations in Eqs. (6.39)-(6.41) and (6.47)-(6.48). Thus the spectra reported for the extended ranges in Figure 3 are not demonstrated to be scheme-independent. The paper should restrict the 'entire theory space' claim to the fully renormalised ranges or supply the missing counterterms and show that the low-energy poles are unaffected.
  3. [Section 6.4, Eqs. (6.38), (6.52)-(6.55)] In the regime M̂±≈O(ε), M̂∓≈O(ε^{-1}), the text states that the correlators are simplified under the assumption ω∼ε^2. However, Eq. (6.38), which is the starting point for this regime, was derived in Section 6.2.2 under the assumption ω∼ε. The dispersion relations (6.54)-(6.55) following from Eqs. (6.52)-(6.53) have modes with ω∼ε (attenuated sound), not ω∼ε^2. The stated scaling is therefore internally inconsistent and should be corrected to ω∼ε. This matters because the identification of the pole collision and the attenuation of sound in the massive theory is one of the paper's central results; as written, the reader cannot tell which terms are genuinely subleading.
minor comments (5)
  1. [Section 6.4, after Eqs. (6.52) and (6.53)] The phrase 'assuming ... ω∼ε^2' appears in both places; if the poles are indeed O(ε), this should be corrected to ω∼ε for consistency with Eq. (6.38).
  2. [Section 6.5, first paragraph] The statement that the low-energy spectrum has been determined for the 'entire theory space (excluding λ=3)' should also mention the other restrictions stated in Section 3.2: the exclusion of isolated values where Δ+−Δ− is an even integer, and the assumption |m^2|<<1.
  3. [Figure 3] The legend is difficult to decode; the coloured hatching lines and dots are not all explained in the caption. A table or an explicit step-by-step example would improve readability.
  4. [Section 2.3.3, Eq. (2.47)] The notation S_new[Ψ,Φ̃]≡S_new[Ψ] is confusing. Please state explicitly that the dependence on Φ̃ drops out after the field redefinition, and specify that Θ(0) is assumed nonvanishing and invertible.
  5. [Section 3.2.1, Eqs. (3.22)-(3.23)] The convention for the ellipsis is intricate and hard to follow. A short worked example of the convention would help the reader verify the subleading structure.

Circularity Check

0 steps flagged

No significant circularity: the spectra are derived from specified bulk actions and deformation scales, not fitted or defined by the target results.

full rationale

The paper's derivation chain is self-contained: it starts from explicit bulk actions (Maxwell action (3.4) for massless p-forms and the Higher Stückelberg action (3.8) for massive p-forms), solves the near-boundary and near-horizon equations, performs holographic renormalisation, imposes Robin boundary conditions controlled by deformation scales M, and then computes retarded correlators and their poles. The inputs are the bulk mass m^2, the deformation scales M, the spacetime dimension, the form rank, and the quantisation scheme; the outputs are dispersion relations, pole collisions, emergent photons, and duality maps. No parameter is fitted to the predicted spectra, and no result is defined in terms of the quantity it is supposed to predict. The massless limit in Section 6.5 is used only as a consistency check: massive correlators reduce to the independently computed massless correlators under the stated identifications of M, and the massive results are not constructed from the massless ones. The dualities in Section 5 are derived from explicit Hodge-star field redefinitions of the bulk equations of motion, not imported from a self-citation or uniqueness theorem. External works such as [29], [69], and [71] are cited as benchmarks or comparisons, not as load-bearing justification for the new p-form results. The only self-citation, [72], appears in the outlook as a suggested future extension and does not support any central claim. The single-p-form truncation is a structural modelling assumption about the completeness of the low-energy effective theory; that is a physical approximation and a possible correctness risk, but it is not circular because the paper does not use the desired spectra to justify the truncation. Overall, no circular step satisfying the required evidence threshold is present.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

All parameters are theory inputs rather than fitted values. The main load-bearing modeling choice is the massive-p-form description of weakly broken higher-form symmetry. The paper introduces no new particles, forces, or conserved quantities beyond the existing higher-form symmetry framework.

free parameters (4)
  • M1 / M2 (massless double-trace couplings)
    Couplings of the double-trace deformations in Eq. (4.10); dimensionless versions M̂1/2 are scanned from weak to strong. They are theory inputs, not fitted to external data.
  • M± / M∓ (massive double-trace couplings)
    Deformation couplings in Eqs. (4.31), (5.16), (5.17); scanned across regimes. Inputs controlling quasihydrodynamic relaxation gaps.
  • m² (bulk mass squared)
    Small mass, |m²|≪1, controlling explicit breaking of the higher-form symmetry. A model input, not fitted to data.
  • λ̄ = d+1−2q and λ = d+1−2n
    Labels of the theory space determined by spacetime dimension and form rank. Not fitted; used to organize the spectrum.
axioms (6)
  • standard math Standard AdS/CFT dictionary, GKPW path integral, large-N limit, and holographic renormalisation apply to p-form bulk theories.
    Sections 2–4 rely on these as background results; they are not re-derived in the paper.
  • domain assumption A single massive p-form / Higher Stückelberg action is the complete low-energy holographic dual of a weakly broken higher-form symmetry.
    Section 2.3.3 linearises around an intact-symmetry background; Eq. (3.8) defines the model. If other light modes or nonlinear defect dynamics couple, the spectra change.
  • ad hoc to paper Double-trace deformations are implemented by Robin boundary conditions and are mutually exclusive: M1 and M2 cannot both be nonzero; M+ and M− cannot both be nonzero.
    Sections 4.1 and 4.2 state the deformations are only valid non-simultaneously; this restriction is specific to the paper's renormalisation prescription.
  • domain assumption Hydrodynamic limit: ω/(4πT)≪1, k∼m∼ε≪1, radial derivatives dominate, and ingoing horizon boundary conditions give retarded correlators.
    Section 6.1–6.2, Eqs. (6.10)–(6.13); the derived dispersion relations are only valid in this low-energy scaling regime.
  • ad hoc to paper Restriction to |m²|≪1 with Δ+−Δ− not an even integer, and exclusion of λ=3.
    Section 3.2 restricts to case (i); Section 6.5 explicitly excludes λ=3. Special cases are deferred to future work.
  • domain assumption No additional bulk couplings (Chern-Simons, H∧H, H∧F, F∧F) contribute at leading order where they are allowed.
    Section 3.1 notes such terms can be available for 1≤d−2n≤3 but are ignored; this is a deliberate model choice.

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read the original abstract

We study the low-energy dynamics of systems with exact and approximate higher-form symmetries using Gauge-gravity duality. These symmetries are realised holographically via generalised Maxwell/Proca theories for massless/massive $p$-forms in AlAdS spacetimes. Double-trace deformations of the boundary theory are considered via appropriate boundary conditions. We compute thermal correlation functions in isotropic black brane backgrounds to characterise the near equilibrium regimes of the dual boundary theories. In the vanishing-mass limit, the theory exhibits a hydrodynamic regime for weak double-trace deformations (relative to a scale set by the temperature) and a quasihydrodynamic regime for strong deformations. Turning on the bulk mass gives rise instead to a triad of quasihydrodynamic regimes controlled by both the mass and the double-trace coupling. In general, we find the low-energy spectra to be constrained by pole collisions, emergent symmetries and duality relations, the latter originating in part from Hodge-type dualities in the bulk. For nonzero mass, there is an additional strong/weak duality of the double-trace couplings. We further show, in the low-density limit of background charge, that relevant deformations are necessary for stable diffusion of sufficiently high-dimensional charged objects.

Figures

Figures reproduced from arXiv: 2509.26583 by Andr\'e Oliveira Pinheiro.

Figure 1
Figure 1. Figure 1: 1-form symmetry with defects: on the left, time is indicated as running vertically; in the middle, two infinitely extended strings and their worldsheets are shown — the 1-form symmetry is reflected in the fact that the number of intersections between the worldsheets and a codimension-2 hypersurface is topological; on the right, the symmetry is broken by a 0-dimensional defect consisting of a junction from … view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of a double-trace deformation’s effect on thermal spectra (at low-energies) of holographic duals to p-forms in the electric quantisation: m2 = 0 (top) and |m2 | ≪ 1 (bottom). This section contains the main results of this paper, which are more deeply summarised in Section 6.5. There, we also examine how the massless correlators can be obtained from their massive counterpart by deriving a parti… view at source ↗
Figure 3
Figure 3. Figure 3: A schematic depiction of the modes that populate the spectrum of each theory at low energies. On the left, for d ≥ 2, we have spectra of duals to the massless theories with electric (magnetic) quantisation on top (bottom). Likewise, for 0 ≤ n ≤ d − 2 and d ≥ 3 the right-hand side refers to the massive case where electric (magnetic) quantisation is at the bottom (top). While undeformed theories sit at the λ… view at source ↗

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  1. Approximate higher-form symmetries and dualities of massive p-forms in the holographic bulk

    hep-th 2026-05 unverdicted novelty 5.0

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Reference graph

Works this paper leans on

73 extracted references · 50 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized global symmetries, Journal of High Energy Physics2015(2015)

    2015

  2. [2]

    Cordova, T.T

    C. Cordova, T.T. Dumitrescu, K. Intriligator and S.-H. Shao, Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond, in Snowmass 2021, 5, 2022 [2205.09545]

    Pith/arXiv arXiv 2021

  3. [3]

    Landau, On the theory of phase transitions, Zh

    L.D. Landau, On the theory of phase transitions, Zh. Eksp. Teor. Fiz.7(1937) 19

    1937

  4. [4]

    McGreevy, Generalized Symmetries in Condensed Matter, Ann

    J. McGreevy, Generalized Symmetries in Condensed Matter, Ann. Rev. Condensed Matter Phys.14(2023) 57 [2204.03045]

    Pith/arXiv arXiv 2023

  5. [5]

    Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries, 2308.00747

    S.-H. Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries, 2308.00747

    Pith/arXiv arXiv

  6. [6]

    Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries, Phys

    S. Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries, Phys. Rept.1063(2024) 1 [2305.18296]

    Pith/arXiv arXiv 2024

  7. [7]

    Brennan and S

    T.D. Brennan and S. Hong, Introduction to Generalized Global Symmetries in QFT and Particle Physics, 2306.00912

    Pith/arXiv arXiv

  8. [8]

    Bhardwaj, L.E

    L. Bhardwaj, L.E. Bottini, L. Fraser-Taliente, L. Gladden, D.S.W. Gould, A. Platschorre et al., Lectures on generalized symmetries, Phys. Rept.1051(2024) 1 [2307.07547]

    Pith/arXiv arXiv 2024

  9. [9]

    Gomes, An introduction to higher-form symmetries, SciPost Phys

    P.R.S. Gomes, An introduction to higher-form symmetries, SciPost Phys. Lect. Notes 74(2023) 1 [2303.01817]

    Pith/arXiv arXiv 2023

  10. [10]

    Iqbal, Jena lectures on generalized global symmetries: principles and applications, 7, 2024 [2407.20815]

    N. Iqbal, Jena lectures on generalized global symmetries: principles and applications, 7, 2024 [2407.20815]

    Pith/arXiv arXiv 2024

  11. [11]

    Maldacena, The LargeNlimit of superconformal field theories and supergravity, Adv

    J.M. Maldacena, The LargeNlimit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2(1998) 231 [hep-th/9711200]

    Pith/arXiv arXiv 1998

  12. [12]

    Witten, Anti de Sitter space and holography, Adv

    E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys.2(1998) 253 [hep-th/9802150]. 81

    Pith/arXiv arXiv 1998

  13. [13]

    Gubser, I

    S. Gubser, I. Klebanov and A. Polyakov, Gauge theory correlators from non-critical string theory, Physics Letters B428(1998) 105–114

    1998

  14. [14]

    Grozdanov and N

    S. Grozdanov and N. Poovuttikul, Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma, JHEP04(2019) 141 [1707.04182]

    Pith/arXiv arXiv 2019

  15. [15]

    Hofman and N

    D.M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys.4(2018) 005 [1707.08577]

    Pith/arXiv arXiv 2018

  16. [16]

    Grozdanov and N

    S. Grozdanov and N. Poovuttikul, Generalized global symmetries in states with dynamical defects: The case of the transverse sound in field theory and holography, Physical Review D97(2018)

    2018

  17. [17]

    Armas and A

    J. Armas and A. Jain, Viscoelastic hydrodynamics and holography, Journal of High Energy Physics2020(2020)

    2020

  18. [18]

    Grozdanov, D.M

    S. Grozdanov, D.M. Hofman and N. Iqbal, Generalized global symmetries and dissipative magnetohydrodynamics, Phys. Rev. D 95(2017) 096003 [1610.07392]

    Pith/arXiv arXiv 2017

  19. [19]

    Armas and A

    J. Armas and A. Jain, Magnetohydrodynamics as superfluidity, Phys. Rev. Lett.122 (2019) 141603 [1808.01939]

    Pith/arXiv arXiv 2019

  20. [20]

    Glorioso and D.T

    P. Glorioso and D.T. Son, Effective field theory of magnetohydrodynamics from generalized global symmetries, 1811.04879

    Pith/arXiv arXiv

  21. [21]

    Armas and A

    J. Armas and A. Jain, One-form superfluids and magnetohydrodynamics, Journal of High Energy Physics2020(2020)

    2020

  22. [22]

    Delacr´ etaz, D.M

    L.V. Delacr´ etaz, D.M. Hofman and G. Mathys,Superfluids as Higher-form Anomalies, SciPost Phys.8(2020) 047 [1908.06977]

    Pith/arXiv arXiv 2020

  23. [23]

    Delacr´ etaz, B

    L.V. Delacr´ etaz, B. Gout´ eraux and V. Ziogas,Damping of Pseudo-Goldstone Fields, Phys. Rev. Lett.128(2022) 141601 [2111.13459]

    Pith/arXiv arXiv 2022

  24. [24]

    Ammon, D

    M. Ammon, D. Arean, M. Baggioli, S. Gray and S. Grieninger, Pseudo-spontaneousU(1) symmetry breaking in hydrodynamics and holography, JHEP 03(2022) 015 [2111.10305]. 82

    Pith/arXiv arXiv 2022

  25. [25]

    Armas and A

    J. Armas and A. Jain, Approximate higher-form symmetries, topological defects, and dynamical phase transitions, Phys. Rev. D109(2024) 045019 [2301.09628]

    Pith/arXiv arXiv 2024

  26. [26]

    Aharony, M

    O. Aharony, M. Berkooz and E. Silverstein, Multiple trace operators and nonlocal string theories, JHEP08(2001) 006 [hep-th/0105309]

    Pith/arXiv arXiv 2001

  27. [27]

    Boon and S

    J.-P. Boon and S. Yip, Molecular hydrodynamics, McGraw-Hill (1980)

    1980

  28. [28]

    Stephanov and Y

    M. Stephanov and Y. Yin, Hydrodynamics with parametric slowing down and fluctuations near the critical point, Phys. Rev. D98(2018) 036006 [1712.10305]

    Pith/arXiv arXiv 2018

  29. [29]

    Grozdanov, A

    S. Grozdanov, A. Lucas and N. Poovuttikul, Holography and hydrodynamics with weakly broken symmetries, Physical Review D99(2019)

    2019

  30. [30]

    Glorioso and H

    P. Glorioso and H. Liu, Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics, 2018

    2018

  31. [31]

    Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, Journal of Physics A: Mathematical and Theoretical45(2012) 473001

    P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, Journal of Physics A: Mathematical and Theoretical45(2012) 473001

    2012

  32. [32]

    Chaikin and T.C

    P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge (1995)

    1995

  33. [33]

    Forster, Hydrodynamic fluctuations, broken symmetry, and correlation functions, W

    D. Forster, Hydrodynamic fluctuations, broken symmetry, and correlation functions, W. A. Benjamin, Inc. (1975)

    1975

  34. [34]

    Witten, Multitrace operators, boundary conditions, and AdS / CFT correspondence, hep-th/0112258

    E. Witten, Multitrace operators, boundary conditions, and AdS / CFT correspondence, hep-th/0112258

    Pith/arXiv arXiv

  35. [35]

    Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP05(2007) 075 [hep-th/0703152]

    I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP05(2007) 075 [hep-th/0703152]

    Pith/arXiv arXiv 2007

  36. [36]

    Bhattacharyya, S

    S. Bhattacharyya, S. Minwalla, V.E. Hubeny and M. Rangamani, Nonlinear fluid dynamics from gravity, Journal of High Energy Physics2008(2008) 045–045

    2008

  37. [37]

    Avis, C.J

    S.J. Avis, C.J. Isham and D. Storey, Quantum Field Theory in anti-De Sitter Space-Time, Phys. Rev. D18(1978) 3565. 83

    1978

  38. [38]

    Breitenlohner and D.Z

    P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys.144(1982) 249

    1982

  39. [39]

    Breitenlohner and D.Z

    P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-De Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B115(1982) 197

    1982

  40. [40]

    Berkooz, A

    M. Berkooz, A. Sever and A. Shomer, ’Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05(2002) 034 [hep-th/0112264]

    Pith/arXiv arXiv 2002

  41. [41]

    Minces and V.O

    P. Minces and V.O. Rivelles, Energy and the AdS / CFT correspondence, JHEP12 (2001) 010 [hep-th/0110189]

    Pith/arXiv arXiv 2001

  42. [42]

    Mueck, An Improved correspondence formula for AdS / CFT with multitrace operators, Phys

    W. Mueck, An Improved correspondence formula for AdS / CFT with multitrace operators, Phys. Lett. B531(2002) 301 [hep-th/0201100]

    Pith/arXiv arXiv 2002

  43. [43]

    Minces, Multitrace operators and the generalized AdS / CFT prescription, Phys

    P. Minces, Multitrace operators and the generalized AdS / CFT prescription, Phys. Rev. D68(2003) 024027 [hep-th/0201172]

    Pith/arXiv arXiv 2003

  44. [44]

    Sever and A

    A. Sever and A. Shomer, A Note on multitrace deformations and AdS/CFT, JHEP07 (2002) 027 [hep-th/0203168]

    Pith/arXiv arXiv 2002

  45. [45]

    Aharony, M

    O. Aharony, M. Berkooz and B. Katz, Non-local effects of multi-trace deformations in the AdS/CFT correspondence, JHEP 10(2005) 097 [hep-th/0504177]

    Pith/arXiv arXiv 2005

  46. [46]

    Elitzur, A

    S. Elitzur, A. Giveon, M. Porrati and E. Rabinovici, Multitrace deformations of vector and adjoint theories and their holographic duals, JHEP02(2006) 006 [hep-th/0511061]

    Pith/arXiv arXiv 2006

  47. [47]

    Gubser and I.R

    S.S. Gubser and I.R. Klebanov, A Universal result on central charges in the presence of double trace deformations, Nucl. Phys. B656(2003) 23 [hep-th/0212138]

    Pith/arXiv arXiv 2003

  48. [48]

    Hartman and L

    T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP01(2008) 019 [hep-th/0602106]

    Pith/arXiv arXiv 2008

  49. [49]

    Diaz and H

    D.E. Diaz and H. Dorn, 84 Partition functions and double-trace deformations in AdS/CFT, JHEP05(2007) 046 [hep-th/0702163]

    Pith/arXiv arXiv 2007

  50. [50]

    Klebanov and E

    I.R. Klebanov and E. Witten, AdS / CFT correspondence and symmetry breaking, Nucl. Phys. B556(1999) 89 [hep-th/9905104]

    Pith/arXiv arXiv 1999

  51. [51]

    Grozdanov and M

    S. Grozdanov and M. Vrbica, Thermal field theory correlators in the large-Nlimit and the spectral duality relation, 2509.18074

    Pith/arXiv arXiv

  52. [52]

    Klebanov, P

    I.R. Klebanov, P. Ouyang and E. Witten, A Gravity dual of the chiral anomaly, Phys. Rev. D65(2002) 105007 [hep-th/0202056]

    Pith/arXiv arXiv 2002

  53. [53]

    Jimenez-Alba, K

    A. Jimenez-Alba, K. Landsteiner and L. Melgar, Anomalous magnetoresponse and the St¨ uckelberg axion in holography,Phys. Rev. D 90(2014) 126004 [1407.8162]

    Pith/arXiv arXiv 2014

  54. [54]

    Bizdadea and S.O

    C. Bizdadea and S.O. Saliu, The BRST quantization of massive Abelian two form gauge fields, Phys. Lett. B368 (1996) 202

    1996

  55. [55]

    Borsten, M

    L. Borsten, M. Jalali Farahani, B. Jurˇ co, H. Kim, J. N´ aroˇ zn´ y, D. Rist et al., Higher Gauge Theory,2401.05275

    Pith/arXiv arXiv

  56. [56]

    Skenderis, Lecture notes on holographic renormalization, Class

    K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav.19 (2002) 5849 [hep-th/0209067]

    Pith/arXiv arXiv 2002

  57. [57]

    Faulkner and N

    T. Faulkner and N. Iqbal, Friedel oscillations and horizon charge in 1D holographic liquids, JHEP07(2013) 060 [1207.4208]

    Pith/arXiv arXiv 2013

  58. [58]

    Herzog and D.T

    C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP03(2003) 046 [hep-th/0212072]

    Pith/arXiv arXiv 2003

  59. [59]

    Son and A.O

    D.T. Son and A.O. Starinets, Minkowski space correlators in AdS / CFT correspondence: Recipe and applications, JHEP09(2002) 042 [hep-th/0205051]

    Pith/arXiv arXiv 2002

  60. [60]

    van Rees, Dynamics and the gauge/gravity duality, Ph.D

    B.C. van Rees, Dynamics and the gauge/gravity duality, Ph.D. thesis, University of 85 Amsterdam, 2010

    2010

  61. [61]

    Freedman, S.S

    D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography–supersymmetry and a c-theorem, 1999

    1999

  62. [62]

    l’Yi, Correlators of currents corresponding to the massive p-form fields in ads/cft correspondence, Physics Letters B448(1999) 218–226

    W. l’Yi, Correlators of currents corresponding to the massive p-form fields in ads/cft correspondence, Physics Letters B448(1999) 218–226

    1999

  63. [63]

    E. Witten, SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry, in From Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, pp. 1173–1200, 7, 2003 [hep-th/0307041]

    Pith/arXiv arXiv 2003

  64. [64]

    Leigh and A.C

    R.G. Leigh and A.C. Petkou, SL(2,Z) action on three-dimensional CFTs and holography, JHEP12(2003) 020 [hep-th/0309177]

    Pith/arXiv arXiv 2003

  65. [65]

    Yee, A Note on AdS / CFT dual of SL(2,Z) action on 3-D conformal field theories with U(1) symmetry, Phys

    H.-U. Yee, A Note on AdS / CFT dual of SL(2,Z) action on 3-D conformal field theories with U(1) symmetry, Phys. Lett. B598(2004) 139 [hep-th/0402115]

    Pith/arXiv arXiv 2004

  66. [66]

    de Haro and P

    S. de Haro and P. Gao, Electric-magnetic duality and deformations of three-dimensional CFT’s, Phys. Rev. D 76(2007) 106008 [hep-th/0701144]

    Pith/arXiv arXiv 2007

  67. [67]

    de Haro and A.C

    S. de Haro and A.C. Petkou, Holographic Aspects of Electric-Magnetic Dualities, J. Phys. Conf. Ser.110(2008) 102003 [0710.0965]

    Pith/arXiv arXiv 2008

  68. [68]

    DeWolfe and K

    O. DeWolfe and K. Higginbotham, Generalized symmetries and 2-groups via electromagnetic duality inAdS/CF T, Phys. Rev. D103(2021) 026011 [2010.06594]

    Pith/arXiv arXiv 2021

  69. [69]

    Herzog, P

    C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality, and m theory, Physical Review D75(2007)

    2007

  70. [70]

    Hartnoll and C.P

    S.A. Hartnoll and C.P. Herzog, Ohm’s Law at strong coupling: S duality and the cyclotron resonance, Phys. Rev. D76 (2007) 106012 [0706.3228]

    Pith/arXiv arXiv 2007

  71. [71]

    Davison and B

    R.A. Davison and B. Gout´ eraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP01(2015) 039 [1411.1062]. 86

    Pith/arXiv arXiv 2015

  72. [72]

    Davison and A

    R.A. Davison and A. Oliveira Pinheiro, to appear, (2025)

    2025

  73. [73]

    Nelson and B.I

    D.R. Nelson and B.I. Halperin, Dislocation-mediated melting in two dimensions, Phys. Rev. B19(1979) 2457. 87

    1979