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Bosonizing the 2+1d Fermi liquid of noncritical M-theory yields a family of coupled chiral bosons whose density correlators match the exact theory semiclassically.

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2026-07-11 08:07 UTC pith:VPPYP72X

load-bearing objection Solid coadjoint-orbit EFT for the Hořava-Keeler Fermi liquid; light-cone correlators match exactly, eigenvalue three-points only in support so far. the 2 major comments →

arxiv 2607.05143 v1 pith:VPPYP72X submitted 2026-07-06 hep-th cond-mat.str-el

Effective Field Theory of Noncritical M-theory from Bosonization

Patrick Jefferson , Tokiro Numasawa This is my paper
classification hep-th cond-mat.str-el
keywords noncritical M-theorycoadjoint orbit bosonizationFermi liquidchiral bosonsc=1 matrix modeldensity correlatorsinverted harmonic oscillator
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.

Noncritical M-theory is an exact free-fermion definition of a 2+1-dimensional theory that unifies many two-dimensional noncritical string vacua. The paper constructs its low-energy effective theory by bosonizing deformations of the Fermi surface via the coadjoint-orbit method. The resulting action is a continuous family of 1+1d chiral bosons, labeled by classical constants of motion and coupled by interactions that have no one-dimensional counterpart. Tree-level correlators of eigenvalue densities (one-, two- and three-point) and of light-cone densities (all n-point) are shown to agree with the exact Fermi-liquid answers in a suitable large-separation, large-radius limit. The construction is offered as a first step toward a three-dimensional spacetime-gravity dual that would organize the landscape of two-dimensional noncritical strings.

Core claim

Applying coadjoint-orbit bosonization to the double-scaled 2+1d inverted-harmonic-oscillator Fermi liquid produces an effective action of continuously labeled chiral bosons; selected tree-level density correlators of this action reproduce the semiclassical limits of the corresponding exact Fermi-liquid correlators.

What carries the argument

The coadjoint orbit of the semiclassical w_∞ algebra of phase-space functions, parametrized by a bosonic field φ that deforms the ground-state distribution; after gauge fixing, the action and density operators are expanded order-by-order in φ and evaluated on the Fermi surface.

Load-bearing premise

Agreement of a finite set of tree-level density correlators in the semiclassical regime is taken as evidence that the truncated bosonized action correctly captures the low-energy physics of noncritical M-theory.

What would settle it

An exact three-point eigenvalue-density correlator computed in the Fermi liquid that fails to match the full functional form (not merely the support) of the corresponding tree-level bosonized expression at large separation and large radius.

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

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 / 4 minor

Summary. The paper applies the coadjoint-orbit bosonization of Delacretaz–Du–Mehta–Son to the double-scaled 2+1d inverted-harmonic-oscillator Fermi liquid that defines noncritical M-theory (Hořava–Keeler). After recovering the Das–Jevicki collective field theory as a 1+1d check (Sec. 4), it constructs the effective action of a continuous family of chiral bosons labeled by classical constants of motion, first in p-gauge (quadratic + cubic WZW and Hamiltonian terms, Sec. 5.2) and then in h-gauge (Sec. 5.3). Tree-level correlators of two classes of density operators are compared with exact Fermi-liquid Wick contractions and resolvent saddles: light-cone densities match to all orders (connected n≥3 vanish identically, Sec. 6.4); eigenvalue one- and two-point functions agree asymptotically at large |λ| and large Euclidean separation (Secs. 6.1–6.2); the three-point eigenvalue function is shown to share the same δ-function support on classical trajectories (Sec. 6.3).

Significance. If the truncated bosonized action is a reliable low-energy description, the work supplies a concrete, integrable EFT for the canonical vacuum of noncritical M-theory and a systematic starting point for seeking a 3d gravitational dual. The clean recovery of Das–Jevicki theory, the exact algebraic vanishing of light-cone n≥3 correlators on both sides, and the parameter-free asymptotic match of the eigenvalue two-point function via the resolvent saddle are genuine technical strengths. The construction also makes the residual continuous labels (m,φ) or (φ_σ,ℓ) explicit, clarifying how the higher-dimensional Fermi surface organizes into a continuous family of 1+1d chiral bosons.

major comments (2)
  1. Sec. 6.3 (especially Eqs. (6.29)–(6.45) and the comparison with (3.77)): the three-point eigenvalue correlator is matched only in causal support (δ(s) forcing the three insertions onto a common classical trajectory). The remaining integrals over trajectory parameters (τ_i,m,φ) that would fix the functional prefactor are never evaluated. Because the cubic WZW term (5.31), the new cubic Hamiltonian piece proportional to t_ξ·∂_λ p_F (5.35), and the quadratic density correction ρ^(2) (6.28) are precisely the interactions that distinguish the 2+1d theory from free chiral bosons, agreement of support alone does not yet confirm that those terms are correctly normalized. A leading-order evaluation of the prefactor (or an explicit statement that it is left for future work together with a clear assessment of what is thereby left untested) is needed before the truncated action can be trusted as a s
  2. Secs. 1.2, 6 and 7: the claim that the EFT “correctly captures, at least in the semiclassical regime, the physics of the exact Fermi liquid” rests on tree-level correlators of a weak-field truncation. While the light-cone sector is under complete control and the one- and two-point eigenvalue functions match asymptotically, the paper does not quantify the size of omitted higher-order vertices or loop corrections in the 1/p_F expansion of Appendix D for the three-point (or higher) functions. A short discussion of the regime of validity of the truncation, or an estimate of the first omitted contribution, would strengthen the central claim.
minor comments (4)
  1. Fig. 8 and the accompanying power-counting discussion in Appendix D are helpful but could be cross-referenced more explicitly in Sec. 6.3 so that the reader immediately sees which diagrams are leading at large λ_r.
  2. Notation for the two distinct density operators (ρ(x,λ) versus ρ(u_σ,φ_σ)) is introduced carefully in Sec. 3, yet a short reminder table or sentence at the opening of Sec. 6 would reduce the risk of confusion when the bosonized versions appear.
  3. The Schwarzian tadpole that appears in the Gross–Klebanov Hamiltonian is discarded without comment when comparing to the coadjoint-orbit action in Sec. 4.3; a one-sentence remark on its origin (normal-ordering) would be useful.
  4. Several figures (e.g., Figs. 5, 7, 10) compare exact, saddle, and bosonized results; adding a brief quantitative measure of agreement (relative error or similar) in the captions would make the visual claims more precise.

Circularity Check

0 steps flagged

No significant circularity: bosonized correlators are computed independently from the coadjoint-orbit action and compared to exact free-fermion Wick contractions and resolvent saddles that do not presuppose the EFT.

full rationale

The derivation chain is self-contained. The coadjoint-orbit action (Secs. 4–5) is obtained by applying the external method of Delacretaz–Du–Mehta–Son to the free inverted-oscillator Fermi liquid of Hořava–Keeler; the resulting chiral-boson action (quadratic + cubic WZW/Hamiltonian terms in p-gauge, free in h-gauge) is then used to evaluate tree-level density correlators. These are compared, order by order, to the exact Fermi-liquid correlators obtained from Wick’s theorem on the free fermions (Sec. 3) and the saddle-point resolvent (3.41). No parameters are fitted; the light-cone n-point functions vanish identically on both sides by independent algebraic arguments (Vandermonde degree vs. angular-momentum delta functions); the eigenvalue one- and two-point functions match asymptotically via the same classical action-angle kinematics; the three-point match is only in support (δ(s)), which the paper itself states without claiming a full functional identity. Shared use of action-angle coordinates is a kinematic fact of the integrable single-particle Hamiltonian, not a definitional loop. No self-citation is load-bearing for the central claim, and no uniqueness theorem or ansatz is imported from the authors’ prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 2 invented entities

The paper is a pure theoretical construction. It inherits the coadjoint-orbit formalism, the double-scaled inverted-oscillator Hamiltonian, and the definition of noncritical M-theory from prior literature; it introduces no free numerical parameters and only the standard mathematical structures of phase-space geometry and free-fermion Wick contractions. The sole ‘invented’ objects are the gauge-fixed bosonic fields and the resulting EFT itself.

axioms (4)
  • domain assumption The low-energy dynamics of a Fermi liquid are completely captured by coadjoint orbits of the semiclassical w_∞ algebra of canonical transformations on phase space.
    Taken as given from Delacretaz-Du-Mehta-Son and earlier literature; used throughout Secs. 4–5 to write the bosonic action.
  • domain assumption The double-scaled non-relativistic free-fermion Hamiltonian with inverted harmonic oscillator potential defines noncritical M-theory (Hořava-Keeler).
    The microscopic starting point of the entire paper (Sec. 3.1).
  • ad hoc to paper Tree-level correlators of the truncated weak-field bosonized action are sufficient to test the EFT against the exact Fermi liquid in the semiclassical regime.
    Implicit in the comparison strategy of Sec. 6; higher-loop or non-perturbative corrections are not controlled.
  • standard math Standard free-fermion Wick theorem and the existence of a well-defined Euclidean propagator for the inverted oscillator.
    Used to compute all exact density correlators (App. A, Sec. 3).
invented entities (2)
  • Continuous family of 1+1d chiral bosons labeled by classical constants of motion (m,φ) or (φ_σ,ℓ) no independent evidence
    purpose: To parametrize the residual continuous degrees of freedom of the higher-dimensional Fermi surface after gauge fixing.
    Emerges directly from the coadjoint-orbit construction once the stabilizer is quotiented; no independent experimental handle is claimed.
  • Cubic WZW interaction involving the Reeb vector field on the Fermi surface no independent evidence
    purpose: New interaction term absent in 1d bosonization that couples the chiral bosons.
    Derived in Sec. 5.2.2; its necessity is checked only through the three-point support, not through an independent observable.

pith-pipeline@v1.1.0-grok45 · 68447 in / 3008 out tokens · 31444 ms · 2026-07-11T08:07:39.444053+00:00 · methodology

0 comments
read the original abstract

We extend the coadjoint orbit approach to bosonization systematized by Delacretaz-Du-Mehta-Son to double-scaled non-relativistic Fermi liquids with central inverted harmonic oscillator potential. In 1+1d, this reproduces the Das-Jevicki collective field theory describing quasiparticle excitations of the $c=1$ matrix model. In 2+1d, this yields an effective field theory for noncritical M-theory, namely the 2+1d Fermi liquid proposed by Ho\v{r}ava and Keeler as a unified framework for characterizing noncritical string vacua. With a suitable gauge choice this theory reduces to a continuous family of 1+1d chiral bosons resembling Das-Jevicki collective fields coupled by additional interactions. Utilizing the underlying integrability of noncritical M-theory, we compute select fermion density correlation functions order-by-order in perturbation theory, and provide evidence that they agree with their Fermi liquid counterparts in a suitable semiclassical limit. This represents a step toward an effective spacetime gravity description of noncritical M-theory, which we expect to shed light on both the landscape of 2d noncritical strings and 3d quantum gravity in general.

Figures

Figures reproduced from arXiv: 2607.05143 by Patrick Jefferson, Tokiro Numasawa.

Figure 1
Figure 1. Figure 1: The double scaling limit (2.2) effectively “zooms in” on the quadratic maximum of the potential in (2.1), in the process scaling away other non-universal features while holding fixed the renormalized Fermi level −µ. The figure on the right depicts the inverted harmonic oscillator potential, which is the universal potential that remains after taking the double-scaling limit. In both figures, the shaded regi… view at source ↗
Figure 2
Figure 2. Figure 2: The shaded region is the filled c = 1 string Fermi sea. We can label the state of the Fermi sea in terms of the upper and lower surfaces p±(t, λ), which are indicated for a definite value of λ as an illustration. This is essentially a duplicate of [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The double scaling limit of noncritical M-theory is analogous to the double scaling limit of [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plot of the M-theory resolvent. For both plots we choose [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between the exact resolvent and its saddle-point approximation. The left [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Representative plots of the exact density one-point function. The left panel shows the [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the density two-point function in the ∆ [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Diagrams representing various tree level contributions to the connected correlators of [PITH_FULL_IMAGE:figures/full_fig_p048_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The plot of the exact one-point function compared to the semiclassical one-point function. [PITH_FULL_IMAGE:figures/full_fig_p050_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the density two-point function obtained from the exact fermionic de [PITH_FULL_IMAGE:figures/full_fig_p053_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison between the exact resolvent and the saddle-point approximation includ [PITH_FULL_IMAGE:figures/full_fig_p078_11.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

74 extracted references · 49 linked inside Pith

  1. [1]

    The eleven-dimensional supermembrane revisited,

    P. K. Townsend, “The eleven-dimensional supermembrane revisited,”Phys. Lett. B350 (1995) 184–187,arXiv:hep-th/9501068

    Pith/arXiv arXiv 1995

  2. [2]

    String theory dynamics in various dimensions,

    E. Witten, “String theory dynamics in various dimensions,”Nucl. Phys. B443(1995) 85–126,arXiv:hep-th/9503124

    Pith/arXiv arXiv 1995

  3. [3]

    Heterotic and Type I string dynamics from eleven dimensions,

    P. Horava and E. Witten, “Heterotic and Type I string dynamics from eleven dimensions,” Nucl. Phys. B460(1996) 506–524,arXiv:hep-th/9510209

    Pith/arXiv arXiv 1996

  4. [4]

    Unity of superstring dualities,

    C. M. Hull and P. K. Townsend, “Unity of superstring dualities,”Nucl. Phys. B438(1995) 109–137,arXiv:hep-th/9410167

    Pith/arXiv arXiv 1995

  5. [5]

    M theory as a matrix model: A Conjecture,

    T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, “M theory as a matrix model: A Conjecture,”Phys. Rev. D55(1997) 5112–5128,arXiv:hep-th/9610043

    Pith/arXiv arXiv 1997

  6. [6]

    Supergravity and the large N limit of theories with sixteen supercharges,

    N. Itzhaki, J. M. Maldacena, J. Sonnenschein, and S. Yankielowicz, “Supergravity and the large N limit of theories with sixteen supercharges,”Phys. Rev. D58(1998) 046004, arXiv:hep-th/9802042. 79

    Pith/arXiv arXiv 1998

  7. [7]

    Strings in flat space and pp waves from N=4 superYang-Mills,

    D. E. Berenstein, J. M. Maldacena, and H. S. Nastase, “Strings in flat space and pp waves from N=4 superYang-Mills,”JHEP04(2002) 013,arXiv:hep-th/0202021

    Pith/arXiv arXiv 2002

  8. [8]

    N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,

    O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,”JHEP10(2008) 091, arXiv:0806.1218

    Pith/arXiv arXiv 2008

  9. [9]

    The Large N limit of superconformal field theories and supergravity,

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

    Pith/arXiv arXiv 1998

  10. [10]

    Quantum Geometry of Bosonic Strings,

    A. M. Polyakov, “Quantum Geometry of Bosonic Strings,”Phys. Lett. B103(1981) 207–210

    1981

  11. [11]

    Quantum Geometry of Fermionic Strings,

    A. M. Polyakov, “Quantum Geometry of Fermionic Strings,”Phys. Lett. B103(1981) 211–213

    1981

  12. [12]

    Strings in Less Than One-Dimension,

    M. R. Douglas and S. H. Shenker, “Strings in Less Than One-Dimension,”Nucl. Phys. B 335(1990) 635

    1990

  13. [13]

    Unitary and complex matrix models as 1-d type 0 strings,

    I. R. Klebanov, J. M. Maldacena, and N. Seiberg, “Unitary and complex matrix models as 1-d type 0 strings,”Commun. Math. Phys.252(2004) 275–323,arXiv:hep-th/0309168

    Pith/arXiv arXiv 2004

  14. [14]

    Flux vacua and branes of the minimal superstring,

    N. Seiberg and D. Shih, “Flux vacua and branes of the minimal superstring,”JHEP01 (2005) 055,arXiv:hep-th/0412315

    Pith/arXiv arXiv 2005

  15. [15]

    A Matrix model dual of type 0B string theory in two-dimensions,

    T. Takayanagi and N. Toumbas, “A Matrix model dual of type 0B string theory in two-dimensions,”JHEP07(2003) 064,arXiv:hep-th/0307083

    Pith/arXiv arXiv 2003

  16. [16]

    A New hat for the c=1 matrix model,

    M. R. Douglas, I. R. Klebanov, D. Kutasov, J. M. Maldacena, E. J. Martinec, and N. Seiberg, “A New hat for the c=1 matrix model,” inFrom Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, pp. 1758–1827. 7, 2003.arXiv:hep-th/0307195

    Pith/arXiv arXiv 2003

  17. [17]

    Strings from tachyons: The c=1 matrix reloaded,

    J. McGreevy and H. L. Verlinde, “Strings from tachyons: The c=1 matrix reloaded,”JHEP 12(2003) 054,arXiv:hep-th/0304224

    Pith/arXiv arXiv 2003

  18. [18]

    Fermionic string field theory of c = 1 two-dimensional quantum gravity,

    D. J. Gross and I. R. Klebanov, “Fermionic string field theory of c = 1 two-dimensional quantum gravity,”Nucl. Phys. B352(1991) 671–688

    1991

  19. [19]

    String theory in two-dimensions,

    I. R. Klebanov, “String theory in two-dimensions,” inSpring School on String Theory and Quantum Gravity (to be followed by Workshop). 7, 1991.arXiv:hep-th/9108019

    Pith/arXiv arXiv 1991

  20. [20]

    What is string theory?,

    J. Polchinski, “What is string theory?,” inNATO Advanced Study Institute: Les Houches Summer School, Session 62: Fluctuating Geometries in Statistical Mechanics and Field Theory. 11, 1994.arXiv:hep-th/9411028

    Pith/arXiv arXiv 1994

  21. [21]

    Lectures on 2-D gravity and 2-D string theory,

    P. H. Ginsparg and G. W. Moore, “Lectures on 2-D gravity and 2-D string theory,” in Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles, pp. 277–469. 10, 1993.arXiv:hep-th/9304011

    Pith/arXiv arXiv 1993

  22. [22]

    Matrix models and 2D string theory,

    E. J. Martinec, “Matrix models and 2D string theory,” inNATO Advanced Study Institute: Marie Curie Training Course: Applications of Random Matrices in Physics, pp. 403–457. 10, 2004.arXiv:hep-th/0410136

    Pith/arXiv arXiv 2004

  23. [23]

    Genus one path integral in two-dimensional quantum gravity,

    M. Bershadsky and I. R. Klebanov, “Genus one path integral in two-dimensional quantum gravity,”Phys. Rev. Lett.65(1990) 3088–3091. 80

    1990

  24. [24]

    One-dimensional string theory on a circle,

    D. J. Gross and I. R. Klebanov, “One-dimensional string theory on a circle,”Nucl. Phys. B 344(1990) 475–498

    1990

  25. [25]

    From loops to states in two-dimensional quantum gravity,

    G. W. Moore, N. Seiberg, and M. Staudacher, “From loops to states in two-dimensional quantum gravity,”Nucl. Phys. B362(1991) 665–709

    1991

  26. [26]

    World sheet and space-time physics in two-dimensional (Super)string theory,

    P. Di Francesco and D. Kutasov, “World sheet and space-time physics in two-dimensional (Super)string theory,”Nucl. Phys. B375(1992) 119–170,arXiv:hep-th/9109005

    Pith/arXiv arXiv 1992

  27. [27]

    Exact S matrix for 2-D string theory,

    G. W. Moore, M. R. Plesser, and S. Ramgoolam, “Exact S matrix for 2-D string theory,” Nucl. Phys. B377(1992) 143–190,arXiv:hep-th/9111035

    Pith/arXiv arXiv 1992

  28. [28]

    D-brane decay in two-dimensional string theory,

    I. R. Klebanov, J. M. Maldacena, and N. Seiberg, “D-brane decay in two-dimensional string theory,”JHEP07(2003) 045,arXiv:hep-th/0305159

    Pith/arXiv arXiv 2003

  29. [29]

    Thec= 1 string theory S-matrix revisited,

    B. Balthazar, V. A. Rodriguez, and X. Yin, “Thec= 1 string theory S-matrix revisited,” JHEP04(2019) 145,arXiv:1705.07151 [hep-th]

    Pith/arXiv arXiv 2019

  30. [30]

    Zz instantons and the non-perturbative dual of c = 1 string theory,

    B. Balthazar, V. A. Rodriguez, and X. Yin, “Zz instantons and the non-perturbative dual of c = 1 string theory,”JHEP05(2023) 048,arXiv:1907.07688

    Pith/arXiv arXiv 2023

  31. [31]

    Multi-instanton calculus in c = 1 string theory,

    B. Balthazar, V. A. Rodriguez, and X. Yin, “Multi-instanton calculus in c = 1 string theory,”JHEP05(2023) 050,arXiv:1912.07170

    Pith/arXiv arXiv 2023

  32. [32]

    Fixing an ambiguity in two dimensional string theory using string field theory,

    A. Sen, “Fixing an ambiguity in two dimensional string theory using string field theory,” JHEP03(2020) 005,arXiv:1908.02782

    Pith/arXiv arXiv 2020

  33. [33]

    Divergent− →complex amplitudes in two dimensional string theory,

    A. Sen, “Divergent− →complex amplitudes in two dimensional string theory,”JHEP02 (2021) 086,arXiv:2003.12076

    Pith/arXiv arXiv 2021

  34. [34]

    D-instantons, string field theory and two dimensional string theory,

    A. Sen, “D-instantons, string field theory and two dimensional string theory,”JHEP11 (2021) 061,arXiv:2012.11624

    Pith/arXiv arXiv 2021

  35. [35]

    Normalization of d-instanton amplitudes,

    A. Sen, “Normalization of d-instanton amplitudes,”JHEP11(2021) 077, arXiv:2101.08566

    Pith/arXiv arXiv 2021

  36. [36]

    Instantons in sine-liouville theory,

    S. Alexandrov, R. Mahajan, and A. Sen, “Instantons in sine-liouville theory,”JHEP01 (2024) 141,arXiv:2311.04969

    Pith/arXiv arXiv 2024

  37. [37]

    c= 1 strings as a matrix integral,

    S. Collier, L. Eberhardt, and V. A. Rodriguez, “c= 1 strings as a matrix integral,” arXiv:2604.06301 [hep-th]

    Pith/arXiv arXiv

  38. [38]

    Noncritical M-theory in 2+1 dimensions as a nonrelativistic Fermi liquid,

    P. Horava and C. A. Keeler, “Noncritical M-theory in 2+1 dimensions as a nonrelativistic Fermi liquid,”JHEP07(2007) 059,arXiv:hep-th/0508024

    Pith/arXiv arXiv 2007

  39. [39]

    Thermodynamics of noncritical M-theory and the topological A-model,

    P. Horava and C. A. Keeler, “Thermodynamics of noncritical M-theory and the topological A-model,”Nucl. Phys. B745(2006) 1–28,arXiv:hep-th/0512325

    Pith/arXiv arXiv 2006

  40. [40]

    Strings on AdS(2) and the High-Energy Limit of Noncritical M-Theory,

    P. Horava and C. A. Keeler, “Strings on AdS(2) and the High-Energy Limit of Noncritical M-Theory,”JHEP06(2007) 031,arXiv:0704.2230 [hep-th]

    Pith/arXiv arXiv 2007

  41. [41]

    Luttinger’s Theorem and Bosonization of the Fermi Surface,

    F. D. M. Haldane, “Luttinger’s Theorem and Bosonization of the Fermi Surface,”arXiv e-prints(May, 2005) cond–mat/0505529,arXiv:cond-mat/0505529 [cond-mat.str-el]

    arXiv 2005

  42. [42]

    Bosonization of nonrelativistic fermions and W infinity algebra,

    S. R. Das, A. Dhar, G. Mandal, and S. R. Wadia, “Bosonization of nonrelativistic fermions and W infinity algebra,”Mod. Phys. Lett. A7(1992) 71–84,arXiv:hep-th/9111021. 81

    Pith/arXiv arXiv 1992

  43. [43]

    Nonlinear bosonization of Fermi surfaces: The method of coadjoint orbits,

    L. V. Delacretaz, Y.-H. Du, U. Mehta, and D. T. Son, “Nonlinear bosonization of Fermi surfaces: The method of coadjoint orbits,”Phys. Rev. Res.4no. 3, (2022) 033131, arXiv:2203.05004 [cond-mat.str-el]

    Pith/arXiv arXiv 2022

  44. [44]

    Effective field theory for ersatz Fermi liquids,

    X. Huang, A. Lucas, U. Mehta, and M. Qi, “Effective field theory for ersatz Fermi liquids,” Phys. Rev. B110no. 3, (2024) 035102,arXiv:2402.14066 [cond-mat.str-el]

    Pith/arXiv arXiv 2024

  45. [45]

    Quantizing bosonized Fermi surfaces,

    S. Chen and L. V. Delacretaz, “Quantizing bosonized Fermi surfaces,”Phys. Rev. B113 no. 12, (2026) 125150,arXiv:2510.07583 [cond-mat.str-el]

    arXiv 2026

  46. [46]

    Development in 2-d string theory,

    A. Jevicki, “Development in 2-d string theory,” inWorkshop on String Theory, Gauge Theory and Quantum Gravity. 9, 1993.arXiv:hep-th/9309115

    Pith/arXiv arXiv 1993

  47. [47]

    Matrix quantum mechanics and two-dimensional string theory in nontrivial backgrounds,

    S. Alexandrov, “Matrix quantum mechanics and two-dimensional string theory in nontrivial backgrounds,” other thesis, 9, 2003

    2003

  48. [48]

    Liouville field theory: A Decade after the revolution,

    Y. Nakayama, “Liouville field theory: A Decade after the revolution,”Int. J. Mod. Phys. A 19(2004) 2771–2930,arXiv:hep-th/0402009

    Pith/arXiv arXiv 2004

  49. [49]

    String Field Theory and Physical Interpretation ofD= 1 Strings,

    S. R. Das and A. Jevicki, “String Field Theory and Physical Interpretation ofD= 1 Strings,”Mod. Phys. Lett. A5(1990) 1639–1650

    1990

  50. [50]

    Classical limit of (1+1)-dimensional string theory,

    J. Polchinski, “Classical limit of (1+1)-dimensional string theory,”Nucl. Phys. B362(1991) 125–140

    1991

  51. [51]

    Gravitational scattering in the c = 1 matrix model,

    M. Natsuume and J. Polchinski, “Gravitational scattering in the c = 1 matrix model,”Nucl. Phys. B424(1994) 137–154,arXiv:hep-th/9402156

    Pith/arXiv arXiv 1994

  52. [52]

    Discrete state moduli of string theory from the C=1 matrix model,

    A. Dhar, G. Mandal, and S. R. Wadia, “Discrete state moduli of string theory from the C=1 matrix model,”Nucl. Phys. B454(1995) 541–560,arXiv:hep-th/9507041

    Pith/arXiv arXiv 1995

  53. [53]

    Nonrelativistic fermions, coadjoint orbits of W(infinity) and string field theory at c = 1,

    A. Dhar, G. Mandal, and S. R. Wadia, “Nonrelativistic fermions, coadjoint orbits of W(infinity) and string field theory at c = 1,”Mod. Phys. Lett. A7(1992) 3129–3146, arXiv:hep-th/9207011

    Pith/arXiv arXiv 1992

  54. [54]

    Double scaled field theory at c = 1,

    G. W. Moore, “Double scaled field theory at c = 1,”Nucl. Phys. B368(1992) 557–590

    1992

  55. [55]

    The exact s matrix of the deformed c = 1 matrix model,

    K. Demeterfi, I. R. Klebanov, and J. P. Rodrigues, “The exact s matrix of the deformed c = 1 matrix model,”Phys. Rev. Lett.71(1993) 3409–3412,arXiv:hep-th/9308036

    Pith/arXiv arXiv 1993

  56. [56]

    JT gravity as a matrix integral,

    P. Saad, S. H. Shenker, and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115 [hep-th]

    Pith/arXiv arXiv 1903

  57. [57]

    M. C. Gutzwiller,Chaos in Classical and Quantum Mechanics, vol. 1 ofInterdisciplinary Applied Mathematics. Springer, New York, 1990

    1990

  58. [58]

    Structure of phenomenological Lagrangians. 1.,

    S. R. Coleman, J. Wess, and B. Zumino, “Structure of phenomenological Lagrangians. 1.,” Phys. Rev.177(1969) 2239–2247

    1969

  59. [59]

    Structure of phenomenological Lagrangians. 2.,

    C. G. Callan, Jr., S. R. Coleman, J. Wess, and B. Zumino, “Structure of phenomenological Lagrangians. 2.,”Phys. Rev.177(1969) 2247–2250

    1969

  60. [60]

    Topological strings and integrable hierarchies,

    M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino, and C. Vafa, “Topological strings and integrable hierarchies,”Commun. Math. Phys.261(2006) 451–516,arXiv:hep-th/0312085

    Pith/arXiv arXiv 2006

  61. [61]

    The Quantum Collective Field Method and Its Application to the Planar Limit,

    A. Jevicki and B. Sakita, “The Quantum Collective Field Method and Its Application to the Planar Limit,”Nucl. Phys. B165(1980) 511. 82

    1980

  62. [62]

    Field Theory of Strings as a Collective Field Theory of U(N) Gauge Field,

    B. Sakita, “Field Theory of Strings as a Collective Field Theory of U(N) Gauge Field,” Phys. Rev. D21(1980) 1067

    1980

  63. [63]

    Selfdual Fields as Charge Density Solitons,

    R. Floreanini and R. Jackiw, “Selfdual Fields as Charge Density Solitons,”Phys. Rev. Lett. 59(1987) 1873

    1987

  64. [64]

    Wen,Quantum Field Theory of Many-Body Systems

    X.-G. Wen,Quantum Field Theory of Many-Body Systems. Oxford University Press, 9, 2007

    2007

  65. [65]

    Definition and classification of Fermi surface anomalies,

    D.-C. Lu, J. Wang, and Y.-Z. You, “Definition and classification of Fermi surface anomalies,” Phys. Rev. B109no. 4, (2024) 045123,arXiv:2302.12731 [cond-mat.str-el]

    Pith/arXiv arXiv 2024

  66. [66]

    Excitations and interactions in d = 1 string theory,

    A. M. Sengupta and S. R. Wadia, “Excitations and interactions in d = 1 string theory,”Int. J. Mod. Phys. A6(1991) 1961–1984

    1991

  67. [67]

    A Deformed matrix model and the black hole background in two-dimensional string theory,

    A. Jevicki and T. Yoneya, “A Deformed matrix model and the black hole background in two-dimensional string theory,”Nucl. Phys. B411(1994) 64–96,arXiv:hep-th/9305109

    Pith/arXiv arXiv 1994

  68. [68]

    A Matrix model for AdS(2),

    A. Strominger, “A Matrix model for AdS(2),”JHEP03(2004) 066,arXiv:hep-th/0312194

    Pith/arXiv arXiv 2004

  69. [69]

    Isometry of ads 2 and the c= 1 matrix model,

    P.-M. Ho, “Isometry of ads 2 and the c= 1 matrix model,”Journal of High Energy Physics 2004no. 05, (2004) 008–008

    2004

  70. [70]

    The Conformal limit of the 0A matrix model and string theory on AdS(2),

    O. Aharony and A. Patir, “The Conformal limit of the 0A matrix model and string theory on AdS(2),”JHEP11(2005) 052,arXiv:hep-th/0509221

    Pith/arXiv arXiv 2005

  71. [71]

    Chern-Simons theory and topological strings,

    M. Marino, “Chern-Simons theory and topological strings,”Rev. Mod. Phys.77(2005) 675–720,arXiv:hep-th/0406005

    Pith/arXiv arXiv 2005

  72. [72]

    Nonabelian Bosonization in Two-Dimensions,

    E. Witten, “Nonabelian Bosonization in Two-Dimensions,”Commun. Math. Phys.92(1984) 455–472

    1984

  73. [73]

    E. H. Fradkin,Field Theories of Condensed Matter Physics, vol. 82. Cambridge Univ. Press, Cambridge, UK, 2, 2013

    2013

  74. [74]

    P. A. M. Dirac,The Principles of Quantum Mechanics. The International Series of Monographs on Physics. Clarendon Press, Oxford, 4th ed., 1958. 83

    1958