$E$ and $J$ type $\mathcal{N}=(0,2)$ disordered models and higher-spin symmetry

Liang Wang; Miao Wang

REVIEW 3 major objections 5 minor 36 references

E-type N=(0,2) disordered models are dynamically equivalent to J-type models in the infrared, inheriting the same emergent higher-spin symmetry and vanishing chaos in the large-N limit.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-03 11:13 UTC pith:RGHH3NMN

load-bearing objection A narrow but solid extension of Peng's N=(0,2) SYK analysis; the E-type kernel determinant matches the J-type, but the λ↔λ̄ duality is under-proven. the 3 major comments →

arxiv 2601.06923 v3 pith:RGHH3NMN submitted 2026-01-11 hep-th

E and J type mathcal{N}=(0,2) disordered models and higher-spin symmetry

Liang Wang , Miao Wang This is my paper

classification hep-th

keywords N=(0,2) supersymmetrydisordered modelshigher-spin symmetrySYK modelSchwinger-Dyson equationsladder kernelLandau-Ginzburg theoryholography

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 extends the study of two-dimensional N=(0,2) disordered supersymmetric models to the case where the Fermi-multiplet E-term is present and the J-term is absent. The authors propose a Lagrangian-level duality map between the E-type and J-type models, then verify the equivalence by solving the Schwinger-Dyson equations and computing the ladder kernel matrix for four-point functions. They find that the characteristic determinant of the kernel matrix is identical for both models and independent of the coupling strength. Therefore, the E-type model exhibits the same emergent higher-spin symmetry and absence of chaos as the J-type model in the infrared. This broadens the moduli space of two-dimensional disordered theories with higher-spin structure and adds evidence for a holographic connection to tensionless string theory.

Core claim

The paper establishes a structural duality between two N=(0,2) Landau-Ginzburg disordered models: the E-type model (E ≠ 0, J = 0) and the J-type model (E = 0, J ≠ 0). At the component Lagrangian level, the duality is realized by the map E ↔ −√2 J together with λ ↔ ¯λ, which swaps the roles of the Fermi multiplet's auxiliary field and the superpotential term. By solving the Schwinger-Dyson equations in the conformal IR regime and computing the ladder kernel matrix, the authors show that the characteristic determinant det(k_ij − x·1) is identical for both models and independent of the coupling J². Consequently, the E-type model shares the J-type model's emergent higher-spin symmetry in the lim

What carries the argument

The central mechanism is the duality transformation E ⇔ −√2 J combined with λ ⇔ ¯λ, derived at the component level and expected to hold in the quantum theory. The analysis also relies on a Hubbard-Stratonovich auxiliary field B to linearize the E-term, the conformal ansatz for bi-local Green functions, and the four-point ladder kernel matrix whose characteristic determinant, through the pole condition k = ±1, determines the operator spectrum and detects emergent higher-spin symmetry. The key result is that this determinant is unchanged when passing from the J-type to the E-type model.

Load-bearing premise

The load-bearing premise is that the field map λ ↔ ¯λ, which effectively reverses the chirality of the Fermi multiplet, yields a valid quantum equivalence between the two models; the paper demonstrates this only at the component Lagrangian level and explicitly leaves the formal geometric proof for future work.

What would settle it

Compute the full eigenvalue spectrum of the E-type ladder kernel matrix at finite q and μ, not just its characteristic determinant, and compare with the J-type spectrum at the poles k = ±1. If any eigenvalue differs, or if the four-point function deviates at subleading order in 1/N, the claimed IR equivalence fails. Alternatively, check directly whether λ ↔ ¯λ changes the chirality of the (0,2) theory in a way that alters left-right asymmetric observables.

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

If this is right

The E-type model enlarges the known moduli space of two-dimensional N=(0,2) disordered theories that exhibit emergent higher-spin symmetry.
In the infrared, the E-type model has the same operator spectrum and the same vanishing Lyapunov exponent as the J-type model at the critical value μ → 1/q.
The kernel determinant's independence of J² suggests that the higher-spin structure is robust under variations of the coupling in the E-type model.
The proposed λ ↔ ¯λ symmetry hints at a deeper geometric origin, possibly linked to (0,2) mirror dualities, which could be made precise in future work.
The results provide another piece of evidence for a holographic duality between these disordered models and tensionless string theory.

Where Pith is reading between the lines

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

If the component-level duality holds as a full quantum equivalence, the E-type and J-type models should have identical four-point functions to all orders in 1/N, not just matching kernel determinants—a testable prediction.
The auxiliary field B in the E-type model plays a role analogous to the G field in the J-type model; one could probe whether B acquires dynamics beyond the IR and whether that breaks the equivalence.
A concrete next step, mentioned by the authors, is gauging the U(1) symmetry; this could reveal phase transitions or new dualities that are invisible in the ungauged models.
The geometric interpretation via (0,2) mirror symmetry suggests that similar equivalences might hold in non-disordered Landau-Ginzburg theories, which could be tested independently.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

A narrow but solid extension of Peng's N=(0,2) SYK analysis; the E-type kernel determinant matches the J-type, but the λ↔λ̄ duality is under-proven.

read the letter

The thing to know: this paper adds the E-type configuration (E≠0, J=0) to the N=(0,2) disordered models studied in C. Peng's earlier work, and shows that its IR Schwinger-Dyson equations and ladder kernel determinant match the J-type model. The core new result is Eq. (3.9): the kernel matrices for the two models are different entry-wise but have the same characteristic determinant, so the higher-spin spectrum and the vanishing Lyapunov exponent at μ=1/q are inherited. I checked the algebra on the determinant claim; it holds.

What is genuinely new: the Hubbard-Stratonovich treatment of the ĒE term, the derivation of the E-type SD equations (Eqs. 3.5–3.8), and the explicit kernel matrix comparison. The paper does not try to inflate the result—it leans on [10] for the higher-spin interpretation, which is appropriate. The authors are also upfront that they only establish the E↔J equivalence at the component Lagrangian level and that a formal geometric mapping is out of scope (Sec. 5).

The soft spots: 1. The duality map (Eq. 2.6) includes λ ↔ λ̄. In an (0,2) theory this is not obviously a symmetry of the quantum theory: it exchanges a chiral Fermi multiplet with its anti-chiral conjugate. The authors explicitly leave the geometric proof for the future. For the kernel calculation this matters less than the language suggests—the SD equations are solved directly for the E-type model, and the determinant comparison is a computation, not a consequence of the map. So the main computational result stands even if the duality is interpreted as a correspondence, not a true equivalence. But the abstract says 'establish a duality,' which overshoots what is shown. 2. The numerical evidence for the higher-spin solutions is asserted, not shown. Section 4.2 says 'Numerical verification shows...' with no plots, numerics, or error bars. Since the higher-spin spectrum is inherited from [10] via the determinant equality, this is a minor gap, but a referee should ask for the actual computation or a reference to code. 3. A few steps are compressed: signs in the disorder average (Sec. 3.2) and the N-counting in the GΣ action (Eq. 3.2) are sketched. These are routine but should be explicit for a JHEP paper.

Who this is for: people working on 2d disordered models, SYK holography, and higher-spin/tensionless string transitions. It is a narrow but solid extension of Peng's framework.

My view: the paper should go to peer review. A referee can verify the determinant algebra and push the authors to either sharpen the chirality argument or weaken the 'duality' claim to a 'correspondence in the IR.' The raw computational result is valuable enough to publish with revisions.

Referee Report

3 major / 5 minor

Summary. The paper studies a two-dimensional N=(0,2) disordered Landau-Ginzburg model with a nonzero E-type superpotential and vanishing J-term, extending the J-type analysis of [10]. It proposes a component-level duality map E ↔ −√2 J together with λ ↔ λ̄ (Eq. 2.6), and then computes the IR Schwinger-Dyson equations and the 4×4 ladder kernel matrix for the E-type model. After rescalings, the kernel matrix in Eq. (3.9) has the same characteristic determinant as the J-type model, and the paper concludes that the E-type model is dynamically equivalent in the IR and inherits the emergent higher-spin symmetry and vanishing Lyapunov exponent discussed for the J-type model in [10].

Significance. If valid, the result substantially enlarges the known moduli space of solvable disordered N=(0,2) models and provides an additional concrete boundary example of the proposed holographic link between SYK-like models and tensionless/higher-spin string phases. The E-type SD and kernel computations are performed directly, and the determinant comparison in Eq. (3.9) is explicit and algebraically checkable; the paper does not lean on self-citation, since the J-type input is from [10]. The main limitation is that the interpretive step identifying the two models as dual (0,2) theories rests on the λ ↔ λ̄ exchange, which is not derived from the N=(0,2) superfield structure. The paper itself flags this in Sec. 5.

major comments (3)

[§2.2, Eq. (2.6); §5] The duality map E ↔ −√2J, λ ↔ λ̄ is introduced by comparing component Lagrangians. In N=(0,2), λ is the lowest component of a Fermi superfield satisfying Dbar_+ Λ = √2 E, while λ̄ is the lowest component of the conjugate anti-chiral multiplet. Swapping λ and λ̄ therefore reverses the chirality of the Fermi multiplet; this is not a symmetry of the (0,2) supermultiplet structure unless proved. The SD equations in §3 are computed directly for the E-type model, so they show similarity, not duality, without this map. Since the paper concedes in §5 that a formal geometric mapping is beyond scope, the central claim that the higher-spin spectrum is inherited from [10] is not fully supported. Please provide a superfield-level derivation of Eq. (2.6), or reformulate the conclusions as a structural equivalence with the chirality assumption stated explicitly.
[§3.2, Eq. (3.2)] The passage from the disorder-averaged path integral to the GΣ action is only sketched. The displayed interaction terms after averaging are written without a complete derivation of the signs from the complex Gaussian integral and the Hubbard-Stratonovich linearization, and the factors of M, N, and q are not tracked. These factors enter the SD equations (3.5)–(3.8) and hence the kernel matrix (3.9); an error in this step would change the claimed matching with the J-type model. I ask the authors to display the full derivation, or at least an explicit N,q-counting and sign check, for Eq. (3.2).
[§4.2, Eq. (3.9)] The higher-spin conclusion is inherited from [10] through the determinant identity, but the paper does not present the characteristic determinant or the eigenvalues of the E-type kernel matrix. The statement that (0,s) and (s,0) solve the pole condition in the limit μ → (1/q)^+ is reported as numerical verification without displaying the determinant or the relevant roots. Please provide the explicit characteristic determinant for the matrix in Eq. (3.9), or the eigenvalue data, so that the pole condition k = ±1 can be checked directly for the E-type model.

minor comments (5)

[Abstract; §1] 'While previous studies focused on the J-type model where the E-term ... was discarded' is a sentence fragment; please rewrite. There are also typos such as 'posses' in §5.
[§3.3] The symbol G is used both for the auxiliary F-term and for Green's functions. This is confusing in §3.3; a different symbol for the auxiliary field would improve readability.
[Eq. (3.4)] The displayed relation 'G_i(z) = G_i(z) = (-1)^{2s} G_i(-z)' appears to have identical left and right sides on the first equality; presumably one side should be G_{\bar i}(z). Please correct the notation.
[§3.4] The phrase 'the characteristic determinant is independent of J^2' should be made precise: if the entries k_ij already contain J^2 factors, the pole condition k=1 is not invariant under a global rescaling of the kernel. Please specify the normalization under which the determinant identity is meant.
[§4.1; formatting] Appendix A is referred to as 'Chapter A'; 'Table' is broken in the text. These are minor typographical issues but should be cleaned up.

Circularity Check

0 steps flagged

No significant circularity: the E-type SD equations and kernel determinant are computed directly, and the higher-spin inheritance uses the external benchmark [10].

full rationale

The paper's central derivation is not circular. The duality map E ⇔ −√2 J, λ ⇔ λ̄ (Eq. 2.6) is introduced as an explicit component-level field-redefinition symmetry of the effective Lagrangian, not as a fitted parameter or as a consequence of a self-citation. The Schwinger-Dyson equations in Sec. 3 are derived directly from the E-type action by disorder averaging and a Hubbard-Stratonovich transformation; the replacement G_λ̄ = G_λ is justified by the conformal-weight identity Eq. (3.4) and checked a posteriori in Appendix A as a standard CFT property of conjugate two-point functions, independent of the duality map. The E-type kernel matrix in Eq. (3.9) is computed from the directly derived SD equations, and the equality of the characteristic determinants with the J-type matrix is shown as a concrete algebraic statement, not assumed. The eigenvalues k_ij and the higher-spin spectrum at µ → 1/q are imported from [10] (C. Peng), which is an external, non-self-cited benchmark; using that external result transitively is legitimate and does not reduce the E-type claim to its own inputs. The paper itself flags the unproved geometric origin of λ ↔ λ̄ and the need to examine the map's conditions in Sec. 5 and at the start of Sec. 3; these are validity limitations rather than circular steps. If the chirality issue invalidates the map, the equivalence would be false, but the derivation chain would still not be circular.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 1 invented entities

No parameters are fitted to data; J, q, and μ are model inputs. The paper's central derivation rests on the conformal ansatz and on the λ↔λ̄ duality map, which the authors themselves identify as not fully proven. The auxiliary Hubbard-Stratonovich field B is a computational device, not a new physical entity.

axioms (5)

domain assumption Conformal ansatz G_i(z1,z2)=n_i/((z1−z2)^{2h_i}(z̄1−z̄2)^{2h̃_i}) for IR Green's functions
Assumed in Sec. 3.3 to solve SD equations; standard in SYK but not proven from the dynamics.
domain assumption Ḡ_i(z)=G_i(z)=(-1)^{2s}G_i(−z) identification of conjugate Green's functions
Used in Sec. 3.3 and justified a posteriori in Appendix A; depends on the conformal ansatz and on the λ↔λ̄ identification.
ad hoc to paper λ↔λ̄ exchange is a valid duality map
Introduced in Eq. (2.6); the authors state in Sec. 5 that a formal geometric proof is beyond scope.
standard math Large-N ladder kernel method captures the spectrum of primary operators
Standard SYK technique (Refs [2,3]) imported without re-derivation; used in Sec. 4.
domain assumption Hubbard-Stratonovich transformation −ĒE ≃ B̄B − BE − B̄Ē is valid for the disorder-averaged theory
Introduced in Sec. 3.1 to make Gaussian disorder integrals tractable.

invented entities (1)

Auxiliary field B no independent evidence
purpose: Linearizes the −ĒE term via Hubbard–Stratonovich transformation (Eq. 3.1) so the Gaussian disorder can be integrated.
Not a physical field; its IR two-point function is compared to the J-type auxiliary field G to establish the duality.

pith-pipeline@v1.3.0-alltime-deepseek · 10192 in / 20481 out tokens · 187988 ms · 2026-08-03T11:13:33.332536+00:00 · methodology

0 comments

read the original abstract

In this work, we investigate the emergence of higher-spin structure in 2d $\mathcal{N}=(0,2)$ disordered models. While previous studies focused on the $J$-type model where the $E$-term in the Fermi multiplet was discarded. We extend the discussion to $\mathcal{N}=(0,2)$ disordered models with $E$-type potential. In terms of (disordered) $\mathcal{N}=(0,2)$ Landau-Ginzburg theory, we establish a duality between two models. By solving the Schwinger-Dyson equations and the ladder kernel matrix for 4-point functions, we verify that the $E$-type model is dynamically equivalent to the $J$-type model in the IR regime. Furthermore, we demonstrate that the $E$-type model also exhibits emergent higher-spin symmetry in certain limits. Our results reveal a larger region of the moduli space of 2D $\mathcal{N}=(0,2)$ disordered theories and provides insights into the holographic transition from finite to tensionless strings that can be diagnosed by the emergence of higher-spin symmetries.

discussion (0)

Reference graph

Works this paper leans on

36 extracted references · 19 linked inside Pith

[1]

Sachdev and J

S. Sachdev and J. Ye,Gapless spin-fluid ground state in a random quantum heisenberg magnet,Physical Review Letters70(1993) 3339–3342

1993
[2]

A simple model of quantum holography

A. Kitaev, “A simple model of quantum holography.” Talks at KITP, April 7, and May 27, 2015. – 10 –

2015
[3]

Maldacena and D

J. Maldacena and D. Stanford,Remarks on the sachdev-ye-kitaev model,Physical Review D 94(2016)

2016
[4]

Maldacena, D

J. Maldacena, D. Stanford and Z. Yang,Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,PTEP2016(2016) 12C104 [1606.01857]

Pith/arXiv arXiv 2016
[5]

Rosenhaus,An introduction to the syk model,Journal of Physics A: Mathematical and Theoretical52(2019) 323001

V. Rosenhaus,An introduction to the syk model,Journal of Physics A: Mathematical and Theoretical52(2019) 323001

2019
[6]

M. R. Gaberdiel and R. Gopakumar,Higher Spins & Strings,JHEP11(2014) 044 [1406.6103]

Pith/arXiv arXiv 2014
[7]

M. R. Gaberdiel and R. Gopakumar,String theory as a higher spin theory,Journal of High Energy Physics2016(2016)

2016
[8]

Peng,Vector models and generalized syk models,Journal of High Energy Physics2017 (2017)

C. Peng,Vector models and generalized syk models,Journal of High Energy Physics2017 (2017)

2017
[9]

P. Gao, H. Lin and C. Peng,Quantum chaos from multiple copies of integrable commuting SYK models,Phys. Rev. D112(2025) 066012 [2411.12806]

arXiv 2025
[10]

Peng, N= (0,2) syk, chaos and higher-spins,Journal of High Energy Physics2018(2018)

C. Peng, N= (0,2) syk, chaos and higher-spins,Journal of High Energy Physics2018(2018)

2018
[11]

Ahn and C

C. Ahn and C. Peng,Chiral Algebras of Two-Dimensional SYK Models,JHEP07(2019) 092 [1812.05106]

Pith/arXiv arXiv 2019
[12]

Chang, S

C.-M. Chang, S. Colin-Ellerin, C. Peng and M. Rangamani,A 3d disordered superconformal fixed point,JHEP11(2021) 211 [2108.00027]

Pith/arXiv arXiv 2021
[13]

Chang, S

C.-M. Chang, S. Colin-Ellerin, C. Peng and M. Rangamani,Disordered Vector Models: From Higher Spins to Incipient Strings,Phys. Rev. Lett.129(2022) 011603 [2112.09157]

Pith/arXiv arXiv 2022
[14]

W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev,Supersymmetric Sachdev-Ye-Kitaev models,Phys. Rev. D95(2017) 026009 [1610.08917]

Pith/arXiv arXiv 2017
[15]

C. Peng, M. Spradlin and A. Volovich,A Supersymmetric SYK-like Tensor Model,JHEP05 (2017) 062 [1612.03851]

Pith/arXiv arXiv 2017
[16]

T. Li, J. Liu, Y. Xin and Y. Zhou,Supersymmetric SYK model and random matrix theory, JHEP06(2017) 111 [1702.01738]

Pith/arXiv arXiv 2017
[17]

C. Peng, M. Spradlin and A. Volovich,Correlators in theN= 2Supersymmetric SYK Model,JHEP10(2017) 202 [1706.06078]

Pith/arXiv arXiv 2017
[18]

Bulycheva,N= 2SYK model in the superspace formalism,JHEP04(2018) 036 [1801.09006]

K. Bulycheva,N= 2SYK model in the superspace formalism,JHEP04(2018) 036 [1801.09006]

Pith/arXiv arXiv 2018
[19]

Peng and S

C. Peng and S. Stanojevic,Soft modes inN= 2SYK model,JHEP01(2021) 082 [2006.13961]

Pith/arXiv arXiv 2021
[20]

Heydeman, G

M. Heydeman, G. J. Turiaci and W. Zhao,Phases ofN= 2 Sachdev-Ye-Kitaev models, JHEP01(2023) 098 [2206.14900]

Pith/arXiv arXiv 2023
[21]

Heydeman, Y

M. Heydeman, Y. Liu and G. J. Turiaci,Supersymmetry breaking in SYK and the black hole spectrum,JHEP06(2025) 158 [2408.12138]

Pith/arXiv arXiv 2025
[22]

Murugan, D

J. Murugan, D. Stanford and E. Witten,More on Supersymmetric and 2d Analogs of the SYK Model,JHEP08(2017) 146 [1706.05362]. – 11 –

Pith/arXiv arXiv 2017
[23]

Berkooz, P

M. Berkooz, P. Narayan, M. Rozali and J. Sim´ on,Higher Dimensional Generalizations of the SYK Model,JHEP01(2017) 138 [1610.02422]

Pith/arXiv arXiv 2017
[24]

Turiaci and H

G. Turiaci and H. Verlinde,Towards a 2d QFT Analog of the SYK Model,JHEP10(2017) 167 [1701.00528]

Pith/arXiv arXiv 2017
[25]

M. R. Gaberdiel and R. Gopakumar,An AdS 3 Dual for Minimal Model CFTs,Phys. Rev. D 83(2011) 066007 [1011.2986]

Pith/arXiv arXiv 2011
[26]

Candu and M

C. Candu and M. R. Gaberdiel,Supersymmetric holography on ads3,Journal of High Energy Physics2013(2013)

2013
[27]

Creutzig, Y

T. Creutzig, Y. Hikida and P. B. Rønne,Higher spin ads3 supergravity and its dual cft, Journal of High Energy Physics2012(2012)

2012
[28]

Cao,N= (0,2)higher-spin supergravity in AdS 3,2512.12682

Z. Cao,N= (0,2)higher-spin supergravity in AdS 3,2512.12682

arXiv
[29]

Witten,Phases of n = 2 theories in two dimensions,Nuclear Physics B403(1993) 159–222

E. Witten,Phases of n = 2 theories in two dimensions,Nuclear Physics B403(1993) 159–222

1993
[30]

I. V. Melnikov and S. Sethi,Half-twisted (0, 2) landau-ginzburg models,Journal of High Energy Physics2008(2008) 040–040

2008
[31]

Distler and S

J. Distler and S. Kachru,(0,2) landau-ginzburg theory,Nuclear Physics B413(1994) 213

1994
[32]

Adams, A

A. Adams, A. Basu and S. Sethi,(0,2) duality,Adv. Theor. Math. Phys.7(2003) 865 [hep-th/0309226]

Pith/arXiv arXiv 2003
[33]

Kitaev and S

A. Kitaev and S. J. Suh,The soft mode in the sachdev-ye-kitaev model and its gravity dual, Journal of High Energy Physics2018(2018)

2018
[34]

Bulycheva,A note on the syk model with complex fermions,Journal of High Energy Physics2017(2017)

K. Bulycheva,A note on the syk model with complex fermions,Journal of High Energy Physics2017(2017)

2017
[35]

S. H. Katz and E. Sharpe,Notes on certain (0,2) correlation functions,Commun. Math. Phys.262(2006) 611 [hep-th/0406226]

Pith/arXiv arXiv 2006
[36]

Zhang and C

Z. Zhang and C. Peng,Gauging the complex SYK model,JHEP08(2025) 217 [2502.18595]. A Appendix More On Schwinger Dyson Equations We provide ana posteriorijustification that we can replaceG ¯λ(z) withG λ(z) in the Schwinger-Dyson equations in Eq. (3.5), Σψ =µJ 2Gλ(Gϕ)q−1 , Σϕ =J 2µ (q−1)G λGψ(Gϕ)q−2 +G B Gϕ q−1 , Σλ =J 2Gψ(Gϕ)q−1 , ΣB = J 2 q (Gϕ)q . Another...

arXiv 2025

[1] [1]

Sachdev and J

S. Sachdev and J. Ye,Gapless spin-fluid ground state in a random quantum heisenberg magnet,Physical Review Letters70(1993) 3339–3342

1993

[2] [2]

A simple model of quantum holography

A. Kitaev, “A simple model of quantum holography.” Talks at KITP, April 7, and May 27, 2015. – 10 –

2015

[3] [3]

Maldacena and D

J. Maldacena and D. Stanford,Remarks on the sachdev-ye-kitaev model,Physical Review D 94(2016)

2016

[4] [4]

Maldacena, D

J. Maldacena, D. Stanford and Z. Yang,Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,PTEP2016(2016) 12C104 [1606.01857]

Pith/arXiv arXiv 2016

[5] [5]

Rosenhaus,An introduction to the syk model,Journal of Physics A: Mathematical and Theoretical52(2019) 323001

V. Rosenhaus,An introduction to the syk model,Journal of Physics A: Mathematical and Theoretical52(2019) 323001

2019

[6] [6]

M. R. Gaberdiel and R. Gopakumar,Higher Spins & Strings,JHEP11(2014) 044 [1406.6103]

Pith/arXiv arXiv 2014

[7] [7]

M. R. Gaberdiel and R. Gopakumar,String theory as a higher spin theory,Journal of High Energy Physics2016(2016)

2016

[8] [8]

Peng,Vector models and generalized syk models,Journal of High Energy Physics2017 (2017)

C. Peng,Vector models and generalized syk models,Journal of High Energy Physics2017 (2017)

2017

[9] [9]

P. Gao, H. Lin and C. Peng,Quantum chaos from multiple copies of integrable commuting SYK models,Phys. Rev. D112(2025) 066012 [2411.12806]

arXiv 2025

[10] [10]

Peng, N= (0,2) syk, chaos and higher-spins,Journal of High Energy Physics2018(2018)

C. Peng, N= (0,2) syk, chaos and higher-spins,Journal of High Energy Physics2018(2018)

2018

[11] [11]

Ahn and C

C. Ahn and C. Peng,Chiral Algebras of Two-Dimensional SYK Models,JHEP07(2019) 092 [1812.05106]

Pith/arXiv arXiv 2019

[12] [12]

Chang, S

C.-M. Chang, S. Colin-Ellerin, C. Peng and M. Rangamani,A 3d disordered superconformal fixed point,JHEP11(2021) 211 [2108.00027]

Pith/arXiv arXiv 2021

[13] [13]

Chang, S

C.-M. Chang, S. Colin-Ellerin, C. Peng and M. Rangamani,Disordered Vector Models: From Higher Spins to Incipient Strings,Phys. Rev. Lett.129(2022) 011603 [2112.09157]

Pith/arXiv arXiv 2022

[14] [14]

W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev,Supersymmetric Sachdev-Ye-Kitaev models,Phys. Rev. D95(2017) 026009 [1610.08917]

Pith/arXiv arXiv 2017

[15] [15]

C. Peng, M. Spradlin and A. Volovich,A Supersymmetric SYK-like Tensor Model,JHEP05 (2017) 062 [1612.03851]

Pith/arXiv arXiv 2017

[16] [16]

T. Li, J. Liu, Y. Xin and Y. Zhou,Supersymmetric SYK model and random matrix theory, JHEP06(2017) 111 [1702.01738]

Pith/arXiv arXiv 2017

[17] [17]

C. Peng, M. Spradlin and A. Volovich,Correlators in theN= 2Supersymmetric SYK Model,JHEP10(2017) 202 [1706.06078]

Pith/arXiv arXiv 2017

[18] [18]

Bulycheva,N= 2SYK model in the superspace formalism,JHEP04(2018) 036 [1801.09006]

K. Bulycheva,N= 2SYK model in the superspace formalism,JHEP04(2018) 036 [1801.09006]

Pith/arXiv arXiv 2018

[19] [19]

Peng and S

C. Peng and S. Stanojevic,Soft modes inN= 2SYK model,JHEP01(2021) 082 [2006.13961]

Pith/arXiv arXiv 2021

[20] [20]

Heydeman, G

M. Heydeman, G. J. Turiaci and W. Zhao,Phases ofN= 2 Sachdev-Ye-Kitaev models, JHEP01(2023) 098 [2206.14900]

Pith/arXiv arXiv 2023

[21] [21]

Heydeman, Y

M. Heydeman, Y. Liu and G. J. Turiaci,Supersymmetry breaking in SYK and the black hole spectrum,JHEP06(2025) 158 [2408.12138]

Pith/arXiv arXiv 2025

[22] [22]

Murugan, D

J. Murugan, D. Stanford and E. Witten,More on Supersymmetric and 2d Analogs of the SYK Model,JHEP08(2017) 146 [1706.05362]. – 11 –

Pith/arXiv arXiv 2017

[23] [23]

Berkooz, P

M. Berkooz, P. Narayan, M. Rozali and J. Sim´ on,Higher Dimensional Generalizations of the SYK Model,JHEP01(2017) 138 [1610.02422]

Pith/arXiv arXiv 2017

[24] [24]

Turiaci and H

G. Turiaci and H. Verlinde,Towards a 2d QFT Analog of the SYK Model,JHEP10(2017) 167 [1701.00528]

Pith/arXiv arXiv 2017

[25] [25]

M. R. Gaberdiel and R. Gopakumar,An AdS 3 Dual for Minimal Model CFTs,Phys. Rev. D 83(2011) 066007 [1011.2986]

Pith/arXiv arXiv 2011

[26] [26]

Candu and M

C. Candu and M. R. Gaberdiel,Supersymmetric holography on ads3,Journal of High Energy Physics2013(2013)

2013

[27] [27]

Creutzig, Y

T. Creutzig, Y. Hikida and P. B. Rønne,Higher spin ads3 supergravity and its dual cft, Journal of High Energy Physics2012(2012)

2012

[28] [28]

Cao,N= (0,2)higher-spin supergravity in AdS 3,2512.12682

Z. Cao,N= (0,2)higher-spin supergravity in AdS 3,2512.12682

arXiv

[29] [29]

Witten,Phases of n = 2 theories in two dimensions,Nuclear Physics B403(1993) 159–222

E. Witten,Phases of n = 2 theories in two dimensions,Nuclear Physics B403(1993) 159–222

1993

[30] [30]

I. V. Melnikov and S. Sethi,Half-twisted (0, 2) landau-ginzburg models,Journal of High Energy Physics2008(2008) 040–040

2008

[31] [31]

Distler and S

J. Distler and S. Kachru,(0,2) landau-ginzburg theory,Nuclear Physics B413(1994) 213

1994

[32] [32]

Adams, A

A. Adams, A. Basu and S. Sethi,(0,2) duality,Adv. Theor. Math. Phys.7(2003) 865 [hep-th/0309226]

Pith/arXiv arXiv 2003

[33] [33]

Kitaev and S

A. Kitaev and S. J. Suh,The soft mode in the sachdev-ye-kitaev model and its gravity dual, Journal of High Energy Physics2018(2018)

2018

[34] [34]

Bulycheva,A note on the syk model with complex fermions,Journal of High Energy Physics2017(2017)

K. Bulycheva,A note on the syk model with complex fermions,Journal of High Energy Physics2017(2017)

2017

[35] [35]

S. H. Katz and E. Sharpe,Notes on certain (0,2) correlation functions,Commun. Math. Phys.262(2006) 611 [hep-th/0406226]

Pith/arXiv arXiv 2006

[36] [36]

Zhang and C

Z. Zhang and C. Peng,Gauging the complex SYK model,JHEP08(2025) 217 [2502.18595]. A Appendix More On Schwinger Dyson Equations We provide ana posteriorijustification that we can replaceG ¯λ(z) withG λ(z) in the Schwinger-Dyson equations in Eq. (3.5), Σψ =µJ 2Gλ(Gϕ)q−1 , Σϕ =J 2µ (q−1)G λGψ(Gϕ)q−2 +G B Gϕ q−1 , Σλ =J 2Gψ(Gϕ)q−1 , ΣB = J 2 q (Gϕ)q . Another...

arXiv 2025