arXiv subjects

Chi-Ming Chang

Publications and source records attributed to Chi-Ming Chang.

At least 19 recordsLinked to original sources

arXiv2026

ABJM/BMN Index Matching in the Plane-Wave Limit

We establish coefficientwise equality between the refined supersymmetric indices of ABJM theory and the BMN matrix model in the plane-wave limit at every fixed positive Chern-Simons level k. For multi-membrane families with fixed multiplicities, and hence fixed finite ABJM gauge rank, the equality holds as all longitudinal momenta tend to infinity with their pairwise differences fixed. Scalar-dressed equal-flux ABJM monopoles correspond to BMN vacua of fuzzy-sphere membranes: multiplicities count coincident membranes, whereas flux magnitudes give the momentum per membrane along the M-theory circle. At the index level, the associated Higgs residues yield a diagonal-holonomy integral for the ABJM plane-wave contribution, whose monopole-harmonic kernel agrees with the BMN matrix-harmonic kernel up to the finite BMN upper-spin cutoff. At finite momentum, the full index difference splits into the non-plane-wave remainder and the harmonic tail above this cutoff. Increasing k shifts the former to higher fugacity grade without changing the surviving kernel or the cutoff contribution. This gives a coefficientwise, multi-membrane extension of the earlier single-membrane index relation.

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arXiv2026

Thermal two-point functions in SYK and complex-time singularities

We analyze the finite-temperature two-point function of the large-$N$ SYK model at intermediate couplings away from the infrared fixed point. Specifically, we examine its analytic structure in the complex time plane, tracking the complex-time singularities over a range of temperatures. The location of the leading singularity lies on the imaginary axis. It controls the short-time dynamics of operator complexity, defining an `effective temperature' for the correlator. The next-to-leading singularity lies outside the thermal strip set by the above effective temperature. It has been argued that this could be interpreted in terms of bouncing null geodesics in the emergent black hole geometry. Both these singularities persist all the way down to zero temperature. We discuss our observations and motivate the related emergent geometry using a kinematic space perspective.

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arXiv2026

Mass-Flow Invariance of $Q$-Cohomology in BMN Matrix Quantum Mechanics

We study the dependence of the dynamical supercharges of BMN matrix quantum mechanics on the mass parameter $\mu$. Taking the $\mu$-derivative at fixed canonical matrix variables, we show that the sixteen-component supercharge evolves by the adjoint action of a Hermitian quadratic bosonic operator $\mathcal{K}$, together with the spinor-space factor $i\gamma^{123}$. After projection to a $\gamma^{123}$-eigenspace, this flow integrates to a finite similarity transformation. For the nilpotent component $Q(\mu)=\mathcal Q^4_-(\mu)$, one obtains $Q(\mu)=M(\mu,\mu_0)Q(\mu_0)M(\mu,\mu_0)^{-1}$, giving an algebraic mass-flow non-renormalization statement for the $Q$-cohomology. The corresponding Hilbert-space statement has an analytic qualification, parallel to Witten's argument for supersymmetric quantum mechanics: $M$ is non-unitary and unbounded, so its action on the normalizable domain must be controlled. We formulate a small-step criterion by comparing the quadratic growth of $M$ with the Gaussian falloff of BMN oscillator wavefunctions within each component $\mu>0$ or $\mu<0$. As a concrete check, we evaluate this condition in the $N=2$ theory, whose two vacuum sectors are built on the trivial vacuum and the irreducible fuzzy-sphere vacuum. We also compute the induced $Q_{\rm BPS}$-action on the corresponding BPS letters: in the trivial sector it agrees with the standard BMN-sector BPS-letter differential of $\mathcal{N}=4$ SYM, while in the irreducible sector it vanishes.

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arXiv2026

Finite-$N$ BMN index across all vacuum sectors

We compute the finite-$N$ Witten index of BMN matrix quantum mechanics after summing over all partition-labeled supersymmetric vacuum sectors. Starting from the unitary-matrix integral for each sector, we develop two complementary evaluation methods: a symmetric-group character expansion, which reduces each fixed fugacity order to a finite combinatorial sum, and a residue expansion in which the contributing poles are organized by rooted trees, with a colored-tree generalization for multi-partition sectors. Where practical, direct integration and extraction of the constant term in the expanded integrand give independent coefficient-by-coefficient checks. We evaluate every vacuum sector for $N\leq 9$. In the equal-fugacity expansion, the coefficients near charges $j\sim N^2$ show entropy growth of order $N^2$, and, in this range, the sector sum does not cancel this growth. The finite-$N$ data also reveal a nontrivial sectoral organization: near $j=N^2$, the sector giving the largest contribution changes with $N$, from single-partition sectors at small rank to double-partition sectors starting at $N=5$. We call this phenomenon dominance switching. These results provide quantitative finite-$N$ input for using the BMN index as a diagnostic of protected plane-wave black-hole sectors and suggest a D2 dressed black-hole interpretation in the controlled type-IIA regime, where D0 black-hole sectors are accompanied by macroscopic spherical D2-brane degrees of freedom, analogous to dual dressed black holes in $AdS_5\times S^5$.

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arXiv2026

Super-Chevalley Restriction and Relative Lie Algebra Cohomology over the 2|3 Algebra

Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfrak g\otimes A$ be the corresponding current Lie superalgebra. Motivated by the Chang--Yin description of weak-coupling $1/16$-BPS cohomology in $\mathcal N=4$ super-Yang--Mills, we study the relative Lie algebra cohomology $H^\bullet(\mathfrak g[A],\mathfrak g;\mathbb{C})$. We isolate three finite-rank phenomena. First, the natural $3|2$ super-commuting restriction map, viewed as a super analogue of Chevalley restriction and its commuting-scheme variants, already fails to be an isomorphism for $\mathfrak g=\mathfrak{so}_7$; the obstruction is a non-Cartan class. Second, the same algebra produces explicit fortuitous classes for $\mathfrak{sl}_2$ and $\mathfrak{so}_7$, giving concrete counterexamples to naive stable-image expectations suggested by the type-A Loday--Quillen--Tsygan theorem and its current-algebra refinements. Third, the classical relative cohomologies for the Langlands-dual pair $(\mathfrak{so}_7,\mathfrak{sp}_6)$ are not isomorphic. We then record the conjectural quantum deformation of the differential expected to restore duality, together with first-order evidence pairing the fortuitous and non-Cartan $\mathfrak{so}_7$ classes.

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arXiv2026

Classification of 2D Fermionic Systems with a $\mathbb Z_2$ Flavor Symmetry

We classify superfusion categories describing two-dimensional fermionic systems equipped with the universal fermion-parity symmetry, implemented by a topological defect line (TDL) $Z$, and an additional $\mathbb{Z}_2$ flavor symmetry generated by a $W$ TDL. Depending on whether $W$ is m-type or q-type, its fusion rules lead to three distinct classes, and solving the super-pentagon equations yields 16 consistent superfusion categories. These are labeled by invariants $(\nu_W,\nu_Z,\nu_{WZ})$, which determine the $\mathbb{Z}_8$ anomaly classes of the symmetries generated by $W$, $Z$, and $WZ$. We also provide explicit realizations using multiple Majorana fermions and comment on implications for fermionic CFTs and gapped phases.

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arXiv2025

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

We investigate finite-$N$ BPS cohomology in the D1--D5 CFT, focusing on the sector of fortuitous classes. Analyzing the supercharge cochain complexes in the $N=2$ and $N=3$ theories, we construct several explicit fortuitous classes. We study the decomposition of these cohomology classes into ${\rm SU}(2)_a\times {\rm SU}(2)_b$ representations and conjecture that, at fixed holomorphic weight, those transforming in the largest representation are necessarily fortuitous. Our results also provide strong evidence that the $R$-charge concentration phenomenon extends to the D1--D5 CFT.

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arXiv2025

Violation of S-duality in classical $Q$-cohomology

We study the cohomology of a chiral supercharge $Q$ in the $\mathcal{N}=4$ super-Yang-Mills (SYM) theory at tree level. The cohomology classes correspond one-to-one to the $\frac1{16}$ Bogomol'nyi-Prasad-Sommerfield (BPS) states at one-loop. We argue that monotone classes on the Coulomb branch respect the S-duality between the theories with $\mathrm{SO}(2N+1)$ and $\mathrm{USp}(2N)$ gauge groups, but find an explicit example of a pair of cohomology classes that "violate" the S-duality in the sense that the tree-level $Q$-cohomologies are not isomorphic between the neighborhoods near the two free points. Within this pair, one is a fortuitous class and the other is a monotone chiral ring element. Assuming the non-perturbative validity of S-duality, our results disprove a long-standing conjecture on the one-loop exactness of the $\frac1{16}$-BPS spectrum (including the $\frac1{8}$-BPS chiral ring spectrum) in the $\mathcal{N}=4$ SYM. Mathematically, this shows that, the relative Lie algebra cohomology $H^\bullet(\mathfrak{g}[A],\mathfrak{g})$ is generally not graded-isomorphic to $H^\bullet({}^L\mathfrak{g}[A],{}^L\mathfrak{g})$, where $\mathfrak{g}$ and ${}^L\mathfrak{g}$ are a pair of Langlands dual Lie algebras and $A=\mathbb{C}[z^+,z^-]\otimes\Lambda(\theta_1,\theta_2,\theta_3)$.

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arXiv2025

Fortuity in the D1-D5 system

We reformulate the lifting problem in the D1-D5 CFT as a supercharge cohomology problem, and enumerate BPS states according to the fortuitous/monotone classification. Working in the deformed $T^4$ symmetric orbifold theory, we give precise definitions of monotone and fortuitous cohomology classes generalizing the definitions in \cite{Chang:2024zqi} and illustrate them in the $N=1$ theory. For $N=2$, we construct the cohomology explicitly and match it to the exact BPS partition function. We further describe how to assemble BPS states at smaller $N$ into BPS states at larger $N$, and interpret their holographic duals as black hole bound states and massive stringy excitations on smooth horizonless (e.g. Lunin-Mathur) geometries.

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arXiv2024

Fortuity in SYK Models

We study the fortuity phenomenon in supersymmetric Sachdev-Ye-Kitaev (SYK) models. For generic choices of couplings, all the BPS states in the $\mathcal{N}=2$ SUSY SYK model are fortuitous. The SYK models reveal an intimate connection between fortuity and the Schwarzian description of supersymmetric black holes, reflected in a sharp feature of $R$-charge concentration - microscopically, all the fortuitous states are concentrated in particular charge sectors. We propose that both $R$-charge concentration and the random matrix behavior near the BPS states are key properties of a generic $q$-local supercharge and formulate these as a supercharge chaos conjecture. We expect supercharge chaos to hold universally for supercharges in holographic CFTs near their fortuitous states, potentially providing a microscopic interpretation for the charge constraints of supersymmetric black holes. We also construct SYK models that contain both fortuitous states and monotonous states and contrast their properties, providing further evidence that monotonous states are less chaotic than fortuitous states.

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arXiv2024

Witten index of BMN matrix quantum mechanics

We compute the Witten index of the Berenstein-Maldacena-Nastase matrix quantum mechanics, which counts the number of ground states as well as the difference between the numbers of bosonic and fermionic BPS states with nonzero angular momenta. The Witten index sets a lower bound on the entropy, which exhibits $N^2$ growth that provides strong evidence for the existence of BPS black holes in M-theory, asymptotic to the plane-wave geometry. We also discuss a relation between the Witten index in the infinite $N$ limit and the superconformal index of the Aharony-Bergman-Jafferis-Maldacena theory.

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arXiv2024

Holographic covering and the fortuity of black holes

We propose a classification of BPS states in holographic CFTs into monotone and fortuitous, based on their behaviors in the large $N$ limit. Intuitively, monotone BPS states form infinite sequences with increasing rank $N$, while fortuitous ones exist within finite ranges of consecutive ranks. A precise definition is formulated using supercharge cohomology. We conjecture that under the AdS/CFT correspondence, monotone BPS states are dual to smooth horizonless geometries, and fortuitous ones are responsible for typical black hole microstates and give dominant contributions to the entropy. We present supporting evidence for our conjectures in the ${\cal N}=4$ SYM and symmetric product orbifolds.

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arXiv2023

Split representation in celestial holography

We develop a split representation for celestial amplitudes in celestial holography, by cutting internal lines of Feynman diagrams in Minkowski space. More explicitly, the bulk-to-bulk propagators associated with the internal lines are expressed as a product of two boundary-to-bulk propagators with a coinciding boundary point integrated over the celestial sphere. Applying this split representation, we compute the conformal partial wave and conformal block expansions of celestial four-point functions of massless scalars and photons on the Euclidean celestial sphere. In the $t$-channel massless scalar amplitude, we observe novel intermediate exchanges of staggered modules in the conformal block expansion.

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arXiv2023

On $\frac18$-BPS black holes and the chiral algebra of $\mathcal{N}=4$ SYM

We investigate the existence of $\frac18$-BPS black hole microstates in the $\mathfrak{su}(1,1|2)$ sector of Type IIB string theory on $\mathrm{AdS}_5 \times \mathrm{S}^5$. As will be explained, these states are in one-to-one correspondence with the Schur operators comprising the chiral algebra of $\mathcal{N}=4$ super-Yang-Mills, and a conjecture of Beem et al. implies that the Schur sector only contains graviton operators and hence $\frac18$-BPS black holes do not exist. We scrutinize this conjecture from multiple angles. Concerning the macroscopic counting, we rigorously prove that the flavored Schur index cannot exhibit black hole entropy growth, and provide numerical evidence that the flavored MacDonald index also does not exhibit such growth. Next, we go beyond counting to examine the algebraic structure, beginning by presenting evidence for the well-definedness of the super-$\mathcal{W}$ algebra of Beem et al., then using modular differential equations to argue for an upper bound on the lightest non-graviton operator if existent, and finally performing a systematic construction of cohomologies to recover only gravitons. Along the way, we clarify key aspects of the 4d/2d correspondence using the formalism of the holomorphic topological twist.

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arXiv2023

Disordered $\mathcal{N} = (2, 2)$ Supersymmetric Field Theories

We investigate a large class of $\mathcal{N} = (2, 2)$ supersymmetric field theories in two dimensions, which contains the Murugan-Stanford-Witten model, and can be naturally regarded as a disordered generalization of the two-dimensional Landau-Ginzburg models. We analyze the two and four-point functions of chiral superfields, and extract from them the central charge, the operator spectrum, and the chaos exponent in these models. Some of the models exhibit a conformal manifold parameterized by the variances of the random couplings. We compute the Zamolodchikov metrics on the conformal manifold, and demonstrate that the chaos exponent varies nontrivally along the conformal manifolds. Finally, we introduce and perform some preliminary analysis of a disordered generalization of the gauged linear sigma models, and discuss the low energy theories as ensemble averages of Calabi-Yau sigma models over complex structure moduli space.

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arXiv2023

Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes

We present the first computation of three-point celestial amplitudes in Minkowski space of massless scalars, photons, gluons, and gravitons. Such amplitudes were previously considered to be zero in the literature because the corresponding scattering amplitudes in the plane wave basis vanish for finite momenta due to momentum conservation. However, the delta function for the momentum conservation has support in the soft and colinear regions, and contributes to the Mellin and shadow integrals that give non-zero celestial amplitudes. We further show that when expanding in the (shadow) conformal basis for the incoming (outgoing) particle wave functions, the amplitudes take the standard form of correlators in two-dimensional conformal field theory. In particular, the three-point celestial gluon amplitudes take the form of a three-point function of a spin-one current with two spin-one primary operators, which strongly supports the relation between soft spinning particles and conserved currents. Moreover, the three-point celestial amplitudes of one graviton and two massless scalars take the form of a correlation function involving a primary operator of conformal weight one and spin two, whose level-one descendent is the supertranslation current.

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arXiv2023

Decoding stringy near-supersymmetric black holes

Building on the recent discovery of the first candidate black hole operator in $\mathcal{N}=4$ super-Yang-Mills, we explore the near-supersymmetric aspects of the theory that capture lightly excited, highly stringy black holes. We extend the superspace formalism describing the classically supersymmetric (1/16-BPS) sector of $\mathcal{N}=4$ super-Yang-Mills and compute a large number of one-loop anomalous dimensions. Despite being in the highly stringy regime, we find hints of a gap in the spectrum, similar to that found by a gravitational path integral. We also determine the actual expression of the first candidate black hole operator at weak gauge coupling, going beyond the cohomological construction.

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arXiv2023

Topological Defect Lines in Two Dimensional Fermionic CFTs

We consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of TDLs, called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing feature is an extra one-dimensional Majorana fermion living on the worldline of the TDLs. The properties of TDLs in fermionic CFTs are captured in the mathematical language of the super fusion category. We propose a classification of the rank-2 super fusion categories generalizing the $\mathbb Z_8$ classification for the anomalies of $\mathbb Z_2$ symmetry. We explicitly solve the F-moves for all the nontrivial categories, and derive the corresponding spin selection rules that constrain the spectrum of the defect operators. We find the full set of TDLs in the standard fermionic minimal models and a partial set of TDLs in the two exceptional models, which give CFT realizations to the rank-2 super fusion categories. Finally, we discuss a constraint on the renormalization group flow that preserves a q-type TDL.

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