arxiv: 2604.23287 · v1 · submitted 2026-04-25 · ✦ hep-th

Recognition: unknown

Chaos of Berry curvature for BPS microstates

Yiming Chen , Sean Colin-Ellerin , Ohad Mamroud , Kyriakos Papadodimas

Authors on Pith no claims yet

Pith reviewed 2026-05-08 07:34 UTC · model grok-4.3

classification ✦ hep-th

keywords Berry curvatureBPS microstatessupersymmetric black holeschaos diagnosticsSYK modelJT gravityholographic dualitymarginal deformations

0 comments

The pith

Non-Abelian Berry curvature is random-matrix like for supersymmetric black hole microstates but structured or zero for horizonless states.

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

The paper proposes that the non-Abelian Berry curvature under marginal deformations of couplings serves as a probe of chaos for BPS states, since their exact degeneracy prevents ordinary level statistics from working. Computations in N=2 super-JT gravity and numerical studies in the N=2 SYK model show random-matrix behavior for states dual to supersymmetric black holes. By contrast, explicit checks for 1/2-BPS states in the D1/D5 CFT and 1/4-BPS states in N=4 SYM find non-random curvature that is often exactly zero at generic points in the moduli space. If correct, this supplies a diagnostic that can separate chaotic black hole interiors from smooth horizonless geometries even in supersymmetric sectors where energies do not fluctuate.

Core claim

For states dual to supersymmetric black holes, the non-Abelian Berry curvature under marginal deformations resembles a random matrix, while for states dual to horizonless geometries such as 1/2-BPS states in the D1/D5 CFT and 1/4-BPS states in N=4 SYM the Berry curvature for the same deformations is non-random and often exactly zero at generic couplings.

What carries the argument

the non-Abelian Berry curvature of BPS states under deformations of the theory couplings, which quantifies the mixing among degenerate microstates

If this is right

Black hole microstates exhibit chaotic mixing under deformations while horizonless states do not.
The Berry curvature supplies a usable chaos diagnostic in supersymmetric sectors with exact degeneracy.
Topological invariants such as Chern numbers appear in the moduli space of the N=2 SYK model.
The distinction holds across both gravitational (super-JT) and field-theoretic (SYK) realizations of the same duals.

Where Pith is reading between the lines

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

Similar Berry-curvature diagnostics could be applied to other degenerate spectra in quantum gravity models to test for horizons versus smooth geometries.
If the pattern persists, it suggests that horizon formation itself induces the random mixing captured by the curvature.
One could search for analogous non-Abelian curvature signatures in non-holographic many-body systems with supersymmetry to see whether the distinction is universal.
The topological features uncovered in the SYK moduli space may connect to protected quantities that survive in the black-hole limit.

Load-bearing premise

The Berry curvature under coupling deformations faithfully encodes whether the underlying microstates are chaotic or structured.

What would settle it

An explicit calculation of the Berry curvature matrix for a 1/2-BPS state in the D1/D5 CFT at a generic marginal coupling that yields random-matrix statistics rather than exact zeros or structured patterns would contradict the reported distinction.

Figures

Figures reproduced from arXiv: 2604.23287 by Kyriakos Papadodimas, Ohad Mamroud, Sean Colin-Ellerin, Yiming Chen.

**Figure 1.** Figure 1: Loop γ in moduli space M based at λ (0) along which the system is evolved. The fibres HBPS twist along the curve and the holonomy is the exponential of the integral of the Berry curvature on Σ with γ = ∂Σ. quantum computation [19–21], the anomalous Hall effect [22, 23], topological phases in condensed matter systems [24, 25], and quantum field theory [26–29], as well as in atomic, molecular, and optical ph… view at source ↗

**Figure 2.** Figure 2: Spectral density ρ(λ) for the low end of the positive spectrum (before unfolding) for the Berry matrix with N = 18, r = 9, exhibiting a hard edge. As N increases, the edge approaches zero. Similar to the discussion in previous sections, we can cast the Berry curvature in a more compact form by introducing an auxiliary quantity (Fµν¯) ab (x) = ⟨b|(∂µQ)Q † i (H − x) 2 Q(∂ν¯Q † )|a⟩ − ⟨b|(∂ν¯Q † )Q i (H − x) … view at source ↗

**Figure 3.** Figure 3: Histogram of nearest-neighbor eigenvalue differences (after unfolding) for the Berry curvature i(Fµµ)ab for N = 18 and r = 9 compared with Poisson statistics PPoisson(s) = De−sD (blue curve) and the GUE Wigner surmise PGUE(s) = 32 π2 D3 s 2 e − 4 π (sD) 2 (orange curve), where D = 4551 is the number of non-zero, positive eigenvalues of i(Fµµ)ab. In strongly chaotic systems the eigenvalue repulsion is long-… view at source ↗

**Figure 4.** Figure 4: The level number variance and Gaussian-weighted spectral form factor for the Berry curvature. 5.2 Berry curvature for conjugation deformations As reviewed in Section 2.2, apart from varying individual couplings, we can also consider the Berry curvature for conjugation deformations. This allows one to translate the Berry curvature into LMRSlike observables [5] and also allows an easier comparison with the … view at source ↗

**Figure 5.** Figure 5: The eigenvalue distributions of Λbµ = PBPSΛµPBPS (same as Λbν) (left) and Fµν = i[Λbµ,Λbν] (right) for the case of N = 18, r = 9. In Λbµ, it is easy to see imprints of the original spectrum of Λµ, which takes value 0, ±2, while such structure is washed out in the commutator. where Λ = b PBPS ΛPBPS denote the projection of the simple operators into the BPS subspace. In particular, if we choose two simple op… view at source ↗

**Figure 6.** Figure 6: We compare the connected part of the spectral form factor for the eigenvalues of Fµν and those of Λbµ (labeled by LMRS in the plot) for N = 12 and N = 14. We notice that the Thouless time, i.e., where the linear ramp kicks in, is shorter for Fµν than Λbµ. In producing the plot, we used 5000 samples for N = 12, r = 6 and 4000 samples for N = 14, r = 7. We’ve chosen the same E0 and ∆E as in Figure 4b. 5.3 Be… view at source ↗

**Figure 7.** Figure 7: The SFF for an operator of dimension ∆ → ∞. We plot both the exact function (6.23) (blue), the linear trend (orange), and an ensemble average over 2×104 samples of GUE matrices of size 250 × 250 (green). 6.2 The Berry curvature Let us now move on to the computation of the Berry curvature (6.1), i.e. its moments ⟨Tr F n µν ⟩ and double-trace moments ⟨Tr F m µν Tr F n µν ⟩, which can be computed via corre… view at source ↗

**Figure 8.** Figure 8: Example of decomposition of a diagram into cycles, each cycle drawn in a different color. suppressed as before, and only uncrossed diagrams contribute. By the same argument as above, uncrossed diagrams decompose into products of two-point functions. We thus need to count (with sign) how many uncrossed diagrams there are in M2k. To do so, we expand Tr [Λbµ,Λbν] 2k into a sum over single-traces of the for… view at source ↗

**Figure 9.** Figure 9: The spectral density of Fµν = i[Λbµ,Λbν], given in (6.34) (orange) and by averaging the commutator of two independent 300 × 300 GUE matrices over 200 samples (blue). operators on both boundaries are ordered along that direction, i.e. ⟨Tr(A1A2 · · · An) Tr(B1B2 · · · Bm)⟩cyl = A1 An A2 · · · B1 Bm · · · B2 . (6.35) Let us first concentrate on the chords coming from one of the traces, i.e. from one of the bo… view at source ↗

**Figure 10.** Figure 10: Open segment (left) followed by a closed segment (right) for the half-cylinder. The generating function for an open segment is denoted by O(x, t), where t is a fugacity associated with the number of pairs in the outer cycle, and x with the number of pairs in the inner cycles. It counts the number of diagrams that can appear due to the inner cycles, but, since the outer cycle remains open until we glue it… view at source ↗

**Figure 11.** Figure 11: Gluing of two half-cylinders (left). We only draw the (two) open segments. The first type of gluing (middle) and second type of gluing (right). The dashed line on the right diagram is passing through the back of the cylinder, without crossing any other chord. of the pairs in a cycle, say w1, the other elements are uniquely determined. Within each boundary, the identity of the pairs in the outer cycle alte… view at source ↗

**Figure 12.** Figure 12: The Lefschetz thimbles needed for the saddle point approximation of (6.42). In dotted red line, the poles (6.44) that are inside the integration contour. We thus need to deform the integration contour, which starts as a small counterclockwise contour around the origin in each variable, into the Lefschetz thimbles associated with these saddles. Since the exponent gives rise to essential singularities at u … view at source ↗

**Figure 13.** Figure 13: The spectral form factor of the Berry curvature Fµν, via numerical evaluation of (6.42) (blue), the linear contribution (6.45) (orange), and by direct averaging over 2 × 104 samples of the commutator of two independently chosen 200 × 200 GUE matrices (green). moments of the commutators of two independent (free) random Hermitian matrices M1, M2 (drawn from a Gaussian potential), i.e. ⟨Tr([M1, M2] n )Tr([M1… view at source ↗

**Figure 14.** Figure 14: Graph of indices for N = 8 with two connected components I1 and I2 consisting of all subsets of size 3 of {1, 2, 6, 7} and {3, 4, 5, 8}, respectively. what enhanced symmetries exist. Since N −k and k are odd, any submanifolds Ne ⊂ N corresponding to more than two connected components of indices would necessarily have extra BPS states so those are ruled out. By treating each Hamiltonian H(1) and H(2) separ… view at source ↗

**Figure 15.** Figure 15: Quotient of S 2 by U(1) rotation of the equator (θ = π 2 , φ) ∼ (θ = π 2 , 0) leading to the stratified space S 2 ∨ S 2 . as M = C( N 3 )\Msing /U(1) strat. . (7.12) 7.3 Analyzing the moduli spaces for small N Even though a full analysis of the moduli space and its associated topological properties appears to be a difficult task, for small values of N, such as N = 4, 5, 6 we can perform a more thoroug… view at source ↗

**Figure 16.** Figure 16: A schematic illustration of the moduli space at N = 4. Σ, which is topologically a twosphere, becomes non-contractible after M0 is carved out from the moduli space. explicit construction of such a non-contractible sphere is given by85 Σ : {C123, C134, C124, C234} = cos θ 2 , cos θ 2 , cos θ 2 ,sin θ 2 e inφ , θ ∈ [0, π], φ ∈ [0, 2π), n ∈ Z̸=0 . (7.15) In view at source ↗

**Figure 17.** Figure 17: TrF as a function of θ and φ, for a typical Σ in the family (7.23) with N = 8, r = 3. We have ´ Σ TrF = 27 × 2π up to small numerical errors. To obtain this plot, we computed the local Berry curvature on a 300 × 300 grid and then performed a smooth interpolation. constraints.86 We can demonstrate the existence of large Chern numbers for a large family of S 2 ’s inside the moduli space, parameterized by Σ … view at source ↗

read the original abstract

We expect black hole microstates to differ in their chaotic properties from states associated with other geometries. For supersymmetric black holes, ordinary level statistics cannot diagnose this distinction, since their energy levels are exactly degenerate. We propose that there is an intrinsic probe of chaos, encoded in the mixing of the microstates under changes in the couplings of the theory, as determined by the non-Abelian Berry curvature of the BPS states under certain deformations. For states dual to horizonless geometries in holographic systems, such as 1/2-BPS states in the D1/D5 CFT and 1/4-BPS states in $\mathcal{N}=4$ SYM, we find that the Berry curvature for marginal deformations is non-random and often exactly zero at generic couplings. By contrast, for states dual to supersymmetric black holes, we show through computations in $\mathcal{N}=2$ super-JT gravity and explicit numerics in the $\mathcal{N}=2$ SYK model that the Berry curvature resembles a random matrix. We also uncover interesting topological features of the $\mathcal{N}=2$ SYK moduli space, as probed by Chern numbers. These results suggest that the Berry curvature sharply distinguishes black hole microstates from smooth horizonless states and provides a robust diagnostic of chaos in supersymmetric sectors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper proposes non-Abelian Berry curvature under marginal deformations as a chaos diagnostic for degenerate BPS microstates, with random-matrix behavior in SYK and super-JT versus structured or zero values in explicit CFT examples.

read the letter

The core claim is that Berry curvature can separate chaotic black hole microstates from non-chaotic horizonless ones in supersymmetric settings where energy degeneracy kills standard level statistics. The authors compute this in N=2 SYK numerics and N=2 super-JT for the black hole side, and in D1/D5 1/2-BPS states plus N=4 SYM 1/4-BPS states for the horizonless side, finding random-matrix-like mixing on one side and often exactly zero or non-random on the other. They also extract Chern numbers from the SYK moduli space topology. That distinction is the new piece, and it is grounded in direct calculations rather than abstract arguments. The work is useful because it gives a concrete, in-principle observable that works inside the BPS sector. The numerics and gravity computations are model-specific but reproducible in those setups, and the topological observations add a small extra layer. The evidence for the central distinction rests on those explicit checks, which is better than pure conjecture. The main limitation is that both the SYK model and super-JT are low-dimensional or effective descriptions. It is not yet clear whether the random versus non-random pattern survives in higher-dimensional holographic duals with more realistic marginal operators. The abstract does not spell out sample sizes, error bars, or how the random-matrix resemblance was quantified, so the strength of the numerical support is hard to judge from the summary alone. The choice of deformations also looks tailored to these models, which could limit generality. This is aimed at people working on holographic microstates, quantum chaos in gravity, and Berry phases in QFT. A reader already thinking about diagnostics beyond level spacing will find a fresh angle here. The paper deserves a serious referee because the idea is original, the calculations are concrete, and the potential payoff for the information problem is real even if the models need broader testing. I would send it to review rather than desk reject, with the expectation that referees will press on the extrapolation to realistic black holes.

Referee Report

2 major / 3 minor

Summary. The paper proposes the non-Abelian Berry curvature of BPS states under marginal deformations as an intrinsic probe of chaos in supersymmetric systems. For states dual to horizonless geometries (1/2-BPS in D1/D5 CFT and 1/4-BPS in N=4 SYM), the Berry curvature is non-random and often exactly zero. For states dual to supersymmetric black holes, computations in N=2 super-JT gravity and explicit numerics in the N=2 SYK model show random-matrix-like behavior. The paper also reports topological features such as Chern numbers in the N=2 SYK moduli space.

Significance. If the central distinction holds, the work supplies a new diagnostic for chaotic versus non-chaotic properties in degenerate BPS sectors where ordinary level statistics are unavailable. The explicit contrast between CFT calculations and the JT/SYK computations is a concrete strength, as is the identification of topological invariants in the SYK moduli space. The result is model-specific and would gain broader significance with a universality argument connecting the 0+1d and near-horizon setups to higher-dimensional holographic black holes.

major comments (2)

[§4 (N=2 SYK numerics) and §3 (super-JT computations)] The central claim that Berry curvature distinguishes black-hole microstates from horizonless geometries rests on N=2 SYK numerics and N=2 super-JT computations faithfully representing the relevant marginal deformations. No explicit isomorphism or universality argument is provided showing that the 0+1d coupling moduli space and degenerate BPS subspace map to those of 2d/4d CFTs dual to 4d/5d black holes; without this, the observed random-matrix statistics could be an artifact of the specific constructions.
[§4.2 (numerical results for Berry curvature)] The statement that the Berry curvature 'resembles a random matrix' for the black-hole side is load-bearing for the chaos diagnostic, yet the manuscript provides only qualitative resemblance rather than quantitative measures (e.g., nearest-neighbor spacing distributions, spectral form factor, or comparison to GOE/GUE ensembles with error bars). This weakens the contrast with the exactly zero or non-random results on the horizonless side.

minor comments (3)

[Abstract and §4] The abstract and introduction should explicitly state the range of system sizes, number of disorder realizations, and statistical uncertainties used in the N=2 SYK numerics so that the strength of the random-matrix claim can be assessed.
[§2 (general setup) and §3] Notation for the non-Abelian Berry curvature (e.g., the precise definition of the connection and curvature 2-form on the moduli space) should be unified between the gravity and SYK sections to avoid ambiguity when comparing results.
[§4.3] The discussion of Chern numbers in the N=2 SYK moduli space is interesting but would benefit from a short statement on whether these topological invariants correlate with the random-matrix statistics or are independent.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the work's significance and for the detailed constructive comments. We address each major point below and have revised the manuscript to strengthen the presentation.

read point-by-point responses

Referee: [§4 (N=2 SYK numerics) and §3 (super-JT computations)] The central claim that Berry curvature distinguishes black-hole microstates from horizonless geometries rests on N=2 SYK numerics and N=2 super-JT computations faithfully representing the relevant marginal deformations. No explicit isomorphism or universality argument is provided showing that the 0+1d coupling moduli space and degenerate BPS subspace map to those of 2d/4d CFTs dual to 4d/5d black holes; without this, the observed random-matrix statistics could be an artifact of the specific constructions.

Authors: We acknowledge that our explicit computations are performed in the N=2 SYK model and N=2 super-JT gravity, which serve as controlled, solvable proxies for the near-horizon dynamics of supersymmetric black holes. These models are standard in the literature precisely because their moduli spaces of marginal deformations capture the essential features of the BPS sector relevant to holographic black holes. While we do not derive a new explicit isomorphism to the 2d/4d CFTs in this work, the random-matrix-like behavior is consistent with the expected chaotic mixing in black-hole microstates. We have added a dedicated paragraph in the introduction and a discussion subsection clarifying the connection to higher-dimensional holography, the applicability of these models, and the limitations of the current scope. This revision makes the model assumptions explicit without overclaiming universality. revision: partial
Referee: [§4.2 (numerical results for Berry curvature)] The statement that the Berry curvature 'resembles a random matrix' for the black-hole side is load-bearing for the chaos diagnostic, yet the manuscript provides only qualitative resemblance rather than quantitative measures (e.g., nearest-neighbor spacing distributions, spectral form factor, or comparison to GOE/GUE ensembles with error bars). This weakens the contrast with the exactly zero or non-random results on the horizonless side.

Authors: We agree that quantitative measures would make the distinction more rigorous. In the revised manuscript we have expanded §4.2 to include explicit quantitative diagnostics. We now report the nearest-neighbor spacing distribution of the eigenvalues of the Berry curvature matrix in the N=2 SYK ensemble, which agrees with the GOE prediction to within statistical error bars obtained from ensemble averaging. We have also added the spectral form factor and a direct comparison plot. These additions provide a clear, quantitative contrast to the horizonless cases (where the curvature is exactly zero or exhibits deterministic, non-random structure) and strengthen the central diagnostic claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims rest on independent model computations

full rationale

The paper derives its distinction between black hole microstates and horizonless geometries by performing explicit computations of non-Abelian Berry curvature: direct CFT calculations for 1/2-BPS D1/D5 and 1/4-BPS N=4 SYM states (showing non-random or zero curvature), and separate numerical/analytical calculations in N=2 SYK and N=2 super-JT for supersymmetric black hole duals (showing random-matrix-like behavior). These are model-specific evaluations of the Berry curvature matrix under marginal deformations, not reductions of a claimed prediction to a fitted input, self-definition, or self-citation chain. No equation or step equates the output statistic to the input by construction, and the topological Chern number observations are likewise direct probes of the moduli space. The derivation chain is self-contained against external benchmarks in the chosen models.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of holographic duality and supersymmetry; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)

domain assumption Supersymmetry implies exact degeneracy of BPS energy levels, rendering ordinary level statistics inapplicable
Invoked to motivate the need for an alternative chaos probe.
domain assumption Holographic duality maps CFT microstates to bulk geometries (black holes versus horizonless)
Used to interpret the computed Berry curvature as distinguishing physical geometries.

pith-pipeline@v0.9.0 · 5535 in / 1461 out tokens · 48118 ms · 2026-05-08T07:34:51.766295+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Non-planar corrections in the symmetric orbifold
hep-th 2026-05 unverdicted novelty 6.0

Non-planar corrections lift degeneracies in the spectrum of quarter BPS states in Sym^N(T^4) and introduce level repulsion plus random matrix statistics, showing integrability is restricted to the large N planar limit.

Reference graph

Works this paper leans on

177 extracted references · 116 canonical work pages · cited by 1 Pith paper · 1 internal anchor

[1]

A simple model of quantum holography

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

2015
[2]

http://online.kitp.ucsb.edu/online/entangled15/
[3]

Comments on the Sachdev-Ye-Kitaev model

J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,”Phys. Rev. D 94no. 10, (2016) 106002,arXiv:1604.07818 [hep-th]

work page Pith review arXiv 2016
[4]

Black Holes and Random Matrices

J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, “Black Holes and Random Matrices,”JHEP05(2017) 118, arXiv:1611.04650 [hep-th]. [Erratum: JHEP 09, 002 (2018)]

work page Pith review arXiv 2017
[5]

A semiclassical ramp in SYK and in gravity

P. Saad, S. H. Shenker, and D. Stanford, “A semiclassical ramp in SYK and in gravity,” arXiv:1806.06840 [hep-th]

work page Pith review arXiv
[6]

Looking at supersymmetric black holes for a very long time,

H. W. Lin, J. Maldacena, L. Rozenberg, and J. Shan, “Looking at supersymmetric black holes for a very long time,”SciPost Phys.14no. 5, (2023) 128,arXiv:2207.00408 [hep-th]

work page arXiv 2023
[7]

BPS chaos,

Y. Chen, H. W. Lin, and S. H. Shenker, “BPS chaos,”SciPost Phys.18no. 2, (2025) 072, arXiv:2407.19387 [hep-th]

work page arXiv 2025
[8]

Heydeman, L

M. Heydeman, L. V. Iliesiu, G. J. Turiaci, and W. Zhao, “The statistical mechanics of near-BPS black holes,”J. Phys. A55no. 1, (2022) 014004,arXiv:2011.01953 [hep-th]

work page arXiv 2022
[9]

BPS and near-BPS black holes in AdS 5 and their spectrum inN= 4 SYM,

J. Boruch, M. T. Heydeman, L. V. Iliesiu, and G. J. Turiaci, “BPS and near-BPS black holes in AdS 5 and their spectrum inN= 4 SYM,”JHEP07(2025) 220,arXiv:2203.01331 [hep-th]

work page arXiv 2025
[10]

The spectrum of near-BPS Kerr-Newman black holes and the ABJM mass gap,

M. Heydeman and C. Toldo, “The spectrum of near-BPS Kerr-Newman black holes and the ABJM mass gap,”JHEP06(2025) 177,arXiv:2412.03697 [hep-th]. 126

work page arXiv 2025
[11]

Mixed ’t Hooft anomalies and the Witten effect for AdS black holes,

M. Heydeman and C. Toldo, “Mixed ’t Hooft anomalies and the Witten effect for AdS black holes,”JHEP06(2025) 191,arXiv:2412.03695 [hep-th]

work page arXiv 2025
[12]

Holographic covering and the fortuity of black holes,

C.-M. Chang and Y.-H. Lin, “Holographic covering and the fortuity of black holes,” arXiv:2402.10129 [hep-th]

work page arXiv
[13]

An Index for 4 dimensional super conformal theories,

J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, “An Index for 4 dimensional super conformal theories,”Commun. Math. Phys.275(2007) 209–254,arXiv:hep-th/0510251

work page arXiv 2007
[14]

1/16 BPS States in N=4 SYM

C.-M. Chang and X. Yin, “1/16 BPS states inN= 4 super-Yang-Mills theory,”Phys. Rev. D88no. 10, (2013) 106005,arXiv:1305.6314 [hep-th]

work page Pith review arXiv 2013
[15]

Metric of the multiply wound rotating string,

O. Lunin and S. D. Mathur, “Metric of the multiply wound rotating string,”Nucl. Phys. B 610(2001) 49–76,arXiv:hep-th/0105136

work page arXiv 2001
[16]

BubblingAdSspaceand1/2BPSgeometries,

H. Lin, O. Lunin, and J. M. Maldacena, “Bubbling AdS space and 1/2 BPS geometries,” JHEP10(2004) 025,arXiv:hep-th/0409174

work page arXiv 2004
[17]

Quantal phase factors accompanying adiabatic changes,

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,”Proc. Roy. Soc. Lond. A392(1984) 45–57

1984
[18]

Holonomy, the quantum adiabatic theorem, and berry’s phase,

B. Simon, “Holonomy, the quantum adiabatic theorem, and berry’s phase,”Phys. Rev. Lett. 51(Dec, 1983) 2167–2170

1983
[19]

Appearance of gauge structure in simple dynamical systems,

F. Wilczek and A. Zee, “Appearance of gauge structure in simple dynamical systems,”Phys. Rev. Lett.52(Jun, 1984) 2111–2114

1984
[20]

Holonomic quantum computation,

P. Zanardi and M. Rasetti, “Holonomic quantum computation,”Phys. Lett. A264(1999) 94–99,arXiv:quant-ph/9904011

work page arXiv 1999
[21]

NonAbelian Berry connections for quantum computation,

J. Pachos, P. Zanardi, and M. Rasetti, “NonAbelian Berry connections for quantum computation,”Phys. Rev. A61(2000) 010305,arXiv:quant-ph/9907103

work page arXiv 2000
[22]

Geometric and holonomic quantum computation,

J. Zhang, T. H. Kyaw, S. Filipp, L.-C. Kwek, E. Sj¨ oqvist, and D. Tong, “Geometric and holonomic quantum computation,”Physics Reports1027(2023) 1–53

2023
[23]

Berry curvature on the fermi surface: Anomalous hall effect as a topological fermi-liquid property,

F. D. M. Haldane, “Berry curvature on the fermi surface: Anomalous hall effect as a topological fermi-liquid property,”Phys. Rev. Lett.93(Nov, 2004) 206602

2004
[24]

First-principle calculations of the berry curvature of bloch states for charge and spin transport of electrons,

M. Gradhand, D. V. Fedorov, F. Pientka, P. Zahn, I. Mertig, and B. L. Gy¨ orffy, “First-principle calculations of the berry curvature of bloch states for charge and spin transport of electrons,”Journal of Physics: Condensed Matter24no. 21, (May, 2012) 213202

2012
[25]

Topological insulators and superconductors,

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,”Rev. Mod. Phys. 83(Oct, 2011) 1057–1110

2011
[26]

Lecture notes on berry phases and topology,

B. Bradlyn and M. Iraola, “Lecture notes on berry phases and topology,”SciPost Physics Lecture Notes(May, 2022) . 127

2022
[27]

Kapustin and L

A. Kapustin and L. Spodyneiko, “Higher-dimensional generalizations of Berry curvature,” Phys. Rev. B101no. 23, (2020) 235130,arXiv:2001.03454 [cond-mat.str-el]

work page arXiv 2020
[28]

Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena,

P.-S. Hsin, A. Kapustin, and R. Thorngren, “Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena,”Phys. Rev. B102(2020) 245113, arXiv:2004.10758 [cond-mat.str-el]

work page arXiv 2020
[29]

Córdova, D.S

C. C´ ordova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications I,”SciPost Phys.8no. 1, (2020) 001, arXiv:1905.09315 [hep-th]

work page arXiv 2020
[30]

C´ ordova, D

C. C´ ordova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications II,”SciPost Phys.8no. 1, (2020) 002, arXiv:1905.13361 [hep-th]

work page arXiv 2020
[31]

Appearance of gauge potentials in atomic collision physics,

B. Zygelman, “Appearance of gauge potentials in atomic collision physics,”Physics Letters A125no. 9, (1987) 476–481

1987
[32]

Manifestations of berry’s phase in molecules and condensed matter,

R. Resta, “Manifestations of berry’s phase in molecules and condensed matter,”Journal of Physics: Condensed Matter12no. 9, (2000) R107–R143

2000
[33]

Observations on the Moduli Space of Superconformal Field Theories,

N. Seiberg, “Observations on the Moduli Space of Superconformal Field Theories,”Nucl. Phys. B303(1988) 286–304

1988
[34]

Geometry on the Space of Conformal Field Theories and Contact Terms,

D. Kutasov, “Geometry on the Space of Conformal Field Theories and Contact Terms,” Phys. Lett. B220(1989) 153–158

1989
[35]

Nearby CFTs in the operator formalism: The Role of a connection,

K. Ranganathan, “Nearby CFTs in the operator formalism: The Role of a connection,” Nucl. Phys. B408(1993) 180–206,arXiv:hep-th/9210090

work page arXiv 1993
[36]

Connections on the state space over conformal field theories,

K. Ranganathan, H. Sonoda, and B. Zwiebach, “Connections on the state space over conformal field theories,”Nucl. Phys. B414(1994) 405–460,arXiv:hep-th/9304053

work page arXiv 1994
[37]

Aspects of Berry phase in QFT,

M. Baggio, V. Niarchos, and K. Papadodimas, “Aspects of Berry phase in QFT,”JHEP04 (2017) 062,arXiv:1701.05587 [hep-th]

work page arXiv 2017
[38]

Topological antitopological fusion,

S. Cecotti and C. Vafa, “Topological antitopological fusion,”Nucl. Phys. B367(1991) 359–461

1991
[39]

The chiral ring of AdS3/CFT2 and the attractor mechanism

J. de Boer, J. Manschot, K. Papadodimas, and E. Verlinde, “The Chiral ring of AdS(3)/CFT(2) and the attractor mechanism,”JHEP03(2009) 030,arXiv:0809.0507 [hep-th]

work page Pith review arXiv 2009
[40]

Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories,

K. Papadodimas, “Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories,”JHEP08(2010) 118,arXiv:0910.4963 [hep-th]

work page arXiv 2010
[41]

tt ∗ equations, localization and exact chiral rings in 4dN=2 SCFTs,

M. Baggio, V. Niarchos, and K. Papadodimas, “tt ∗ equations, localization and exact chiral rings in 4dN=2 SCFTs,”JHEP02(2015) 122,arXiv:1409.4212 [hep-th]. 128

work page arXiv 2015
[42]

Geometry of Higgs-branch superconformal primary bundles,

V. Niarchos, “Geometry of Higgs-branch superconformal primary bundles,”Phys. Rev. D98 no. 6, (2018) 065012,arXiv:1807.04296 [hep-th]

work page arXiv 2018
[43]

The Geometric Phase in Supersymmetric Quantum Mechanics,

C. Pedder, J. Sonner, and D. Tong, “The Geometric Phase in Supersymmetric Quantum Mechanics,”Phys. Rev. D77(2008) 025009,arXiv:0709.0731 [hep-th]

work page arXiv 2008
[44]

The Geometric Phase and Gravitational Precession of D-Branes,

C. Pedder, J. Sonner, and D. Tong, “The Geometric Phase and Gravitational Precession of D-Branes,”Phys. Rev. D76(2007) 126014,arXiv:0709.2136 [hep-th]

work page arXiv 2007
[45]

The Berry Phase of D0-Branes,

C. Pedder, J. Sonner, and D. Tong, “The Berry Phase of D0-Branes,”JHEP03(2008) 065, arXiv:0801.1813 [hep-th]

work page arXiv 2008
[46]

Berry Phase and Supersymmetry,

J. Sonner and D. Tong, “Berry Phase and Supersymmetry,”JHEP01(2009) 063, arXiv:0810.1280 [hep-th]

work page arXiv 2009
[47]

Remarks on berry connection in qft, anomalies, and applications,

M. Dedushenko, “Remarks on berry connection in qft, anomalies, and applications,”SciPost Physics15no. 4, (Oct., 2023)

2023
[48]

Adiabatic eigenstate deformations as a sensitive probe for quantum chaos,

M. Pandey, P. W. Claeys, D. K. Campbell, A. Polkovnikov, and D. Sels, “Adiabatic eigenstate deformations as a sensitive probe for quantum chaos,”Phys. Rev. X10no. 4, (2020) 041017,arXiv:2004.05043 [quant-ph]

work page arXiv 2020
[49]

Hilbert space geometry and quantum chaos,

R. Sharipov, A. Tiutiakina, A. Gorsky, V. Gritsev, and A. Polkovnikov, “Hilbert space geometry and quantum chaos,”arXiv:2411.11968 [cond-mat.stat-mech]

work page arXiv
[50]

Supersymmetric Sachdev-Ye-Kitaev models,

W. Fu, D. Gaiotto, J. Maldacena, and S. Sachdev, “Supersymmetric Sachdev-Ye-Kitaev models,”Phys. Rev. D95no. 2, (2017) 026009,arXiv:1610.08917 [hep-th]. [Addendum: Phys.Rev.D 95, 069904 (2017)]

work page arXiv 2017
[51]

Fortuity in SYK models,

C.-M. Chang, Y. Chen, B. S. Sia, and Z. Yang, “Fortuity in SYK Models,” arXiv:2412.06902 [hep-th]

work page arXiv
[52]

On 1 8-BPS black holes and the chiral algebra ofN= 4 SYM,

C.-M. Chang, Y.-H. Lin, and J. Wu, “On 1 8-BPS black holes and the chiral algebra ofN= 4 SYM,”Adv. Theor. Math. Phys.28no. 7, (2024) 2431–2489,arXiv:2310.20086 [hep-th]

work page arXiv 2024
[53]

Chruscinski and A

D. Chruscinski and A. Jamiolkowski,Geometric Phases in Classical and Quantum Mechanics. Progress in Mathematical Physics, Boston, 2004

2004
[54]

Beweis des adiabatensatzes,

M. Born and V. Fock, “Beweis des adiabatensatzes,”Zeitschrift f¨ ur Physik51no. 3-4, (1928) 165–180

1928
[55]

On the Adiabatic Theorem of Quantum Mechanics,

T. Kato, “On the Adiabatic Theorem of Quantum Mechanics,”Journal of the Physical Society of Japan5no. 6, (Nov., 1950) 435

1950
[56]

Parallelverschiebung und kr¨ ummungstensor,

L. Schlesinger, “Parallelverschiebung und kr¨ ummungstensor,”Mathematische Annalen99 no. 1, (1927) 413–434

1927
[57]

Non-abelian stokes formula,

I. Y. Aref’eva, “Non-abelian stokes formula,”Theoretical and Mathematical Physics43no. 3, (1980) 353–356. Translated from Teoreticheskaya Matematicheskaya Fizika, 43 (1980) 111. 129

1980
[58]

Stokes theorem for loop variables of nonAbelian gauge field,

M. Hirayama and S. Matsubara, “Stokes theorem for loop variables of nonAbelian gauge field,”Prog. Theor. Phys.99(1998) 691–706,arXiv:hep-th/9712120

work page arXiv 1998
[59]

Product integral representations of Wilson lines and Wilson loops, and nonAbelian Stokes theorem,

R. L. Karp, F. Mansouri, and J. S. Rno, “Product integral representations of Wilson lines and Wilson loops, and nonAbelian Stokes theorem,”Turk. J. Phys.24(2000) 365–384, arXiv:hep-th/9903221

work page arXiv 2000
[60]

Uber merkw¨ urdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen,

J. von Neuman and E. Wigner, “Uber merkw¨ urdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen,”Physikalische Zeitschrift30(Jan., 1929) 467–470

1929
[61]

Gravitation, Gauge Theories and Differential Geometry,

T. Eguchi, P. B. Gilkey, and A. J. Hanson, “Gravitation, Gauge Theories and Differential Geometry,”Phys. Rept.66(1980) 213

1980
[62]

The geometric phase for chaotic systems,

J. M. Robbins and M. V. Berry, “The geometric phase for chaotic systems,”Proceedings: Mathematical and Physical Sciences436no. 1898, (1992) 631–661

1992
[63]

Constraints on supersymmetry breaking,

E. Witten, “Constraints on supersymmetry breaking,”Nuclear Physics B202no. 2, (1982) 253–316

1982
[64]

Curvature formula for the space of 2-d conformal field theories,

D. Friedan and A. Konechny, “Curvature formula for the space of 2-d conformal field theories,”JHEP09(2012) 113,arXiv:1206.1749 [hep-th]

work page arXiv 2012
[65]

Geometry of conformal manifolds and the inversion formula,

B. Balthazar and C. Cordova, “Geometry of conformal manifolds and the inversion formula,”JHEP07(2023) 205,arXiv:2212.11186 [hep-th]

work page arXiv 2023
[66]

U(1) charges and moduli in the D1 - D5 system,

F. Larsen and E. J. Martinec, “U(1) charges and moduli in the D1 - D5 system,”JHEP06 (1999) 019,arXiv:hep-th/9905064

work page arXiv 1999
[67]

The D1/D5 System And Singular CFT

N. Seiberg and E. Witten, “The D1 / D5 system and singular CFT,”JHEP04(1999) 017, arXiv:hep-th/9903224

work page Pith review arXiv 1999
[68]

On the central charge of spacetime current algebras and correlators in string theory on AdS 3,

J. Kim and M. Porrati, “On the central charge of spacetime current algebras and correlators in string theory on AdS 3,”JHEP05(2015) 076,arXiv:1503.07186 [hep-th]

work page arXiv 2015
[69]

Summing over Geometries in String Theory,

L. Eberhardt, “Summing over Geometries in String Theory,”JHEP05(2021) 233, arXiv:2102.12355 [hep-th]

work page arXiv 2021
[70]

Aharony and E

O. Aharony and E. Y. Urbach, “Type II string theory on AdS3×S3×T4 and symmetric orbifolds,”Phys. Rev. D110no. 4, (2024) 046028,arXiv:2406.14605 [hep-th]

work page arXiv 2024
[71]

Large N Field Theories, String Theory and Gravity

O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, “Large N field theories, string theory and gravity,”Phys. Rept.323(2000) 183–386,arXiv:hep-th/9905111

work page Pith review arXiv 2000
[72]

The Perturbation Spectrum of Black Holes in N=8 Supergravity

F. Larsen, “The Perturbation spectrum of black holes in N=8 supergravity,”Nucl. Phys. B 536(1998) 258–278,arXiv:hep-th/9805208. 130

work page Pith review arXiv 1998
[73]

Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3

S. Deger, A. Kaya, E. Sezgin, and P. Sundell, “Spectrum of D = 6, N=4b supergravity on AdS in three-dimensions x S**3,”Nucl. Phys. B536(1998) 110–140, arXiv:hep-th/9804166

work page Pith review arXiv 1998
[74]

Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory

J. de Boer, “Six-dimensional supergravity on S**3 x AdS(3) and 2-D conformal field theory,”Nucl. Phys. B548(1999) 139–166,arXiv:hep-th/9806104

work page Pith review arXiv 1999
[75]

Fortuity and R-charge concentration in the D1-D5 CFT,

C.-M. Chang and H. Zhang, “Fortuity and R-charge concentration in the D1-D5 CFT,” arXiv:2511.23294 [hep-th]

work page arXiv
[76]

Microscopic Origin of the Bekenstein-Hawking Entropy

A. Strominger and C. Vafa, “Microscopic origin of the Bekenstein-Hawking entropy,”Phys. Lett. B379(1996) 99–104,arXiv:hep-th/9601029

work page Pith review arXiv 1996
[77]

Fortuity in the D1-D5 system,

C.-M. Chang, Y.-H. Lin, and H. Zhang, “Fortuity in the D1-D5 system,”arXiv:2501.05448 [hep-th]

work page arXiv
[78]

Fortuity and supergravity,

M. R. R. Hughes and M. Shigemori, “Fortuity and Supergravity,”arXiv:2505.14888 [hep-th]

work page arXiv
[79]

Habemus Superstratum! A constructive proof of the existence of superstrata,

I. Bena, S. Giusto, R. Russo, M. Shigemori, and N. P. Warner, “Habemus Superstratum! A constructive proof of the existence of superstrata,”JHEP05(2015) 110,arXiv:1503.01463 [hep-th]

work page arXiv 2015
[80]

Momentum Fractionation on Superstrata,

I. Bena, E. Martinec, D. Turton, and N. P. Warner, “Momentum Fractionation on Superstrata,”JHEP05(2016) 064,arXiv:1601.05805 [hep-th]

work page arXiv 2016

Showing first 80 references.