arXiv subjects

Xingyang Yu

Publications and source records attributed to Xingyang Yu.

At least 19 recordsLinked to original sources

arXiv2026

Chiral Spin(7) Sigma Models and Topological Modular Forms

We construct canonical chiral $\mathcal N=(0,1)$ sigma models on Spin(7) manifolds. The Spin(7) structure fixes the rank-seven bundle of the left-moving fermions, whose quadratic index matches the tangent representation, so the internal anomalies cancel while the rank difference leaves the gravitational anomaly of one right-moving Majorana--Weyl fermion. A transverse section of the left-moving bundle has a 1D zero locus with induced String structure, and we compute its class in the first torsion group of topological modular forms. The class is nonzero precisely when the Euler characteristic of the target is odd. The standard Joyce action on the torus has no internal finite-group anomaly and can be gauged to define an exact chiral spin QFT. We show that the orbifold Euler characteristic is even throughout the diagonal Joyce family generated by coordinate reflections and half-shifts preserving the Cayley form. By contrast, a free antiholomorphic quotient of the Fermat sextic is a compact torsion-free Spin(7) target with Euler characteristic 1305 and realizes the nonzero class.

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arXiv2026

Genus-One Rigidity of Bounded Virasoro Pairings for 3D Gravity

Motivated by the proposed relation between 3D gravity and the doubled Virasoro TQFT, and by the associated program of ensemble holography, we ask whether ensemble holography in AdS$_3$/CFT$_2$ can be understood as an average over absolute 2D CFTs obtained by varying the topological boundary condition of the doubled Virasoro TQFT. We show that, at genus one and in the ordinary nondegenerate sector, every vacuum-normalized, modular-invariant genus-one pairing that acts boundedly on the auxiliary $L^2$ label space is diagonal. Under the ordinary block-diagonal vacuum--continuum ansatz, the same conclusion holds for entrywise-positive, modular-invariant Borel-measure pairings satisfying the two vacuum marginals, without assuming absolute continuity or boundedness. The bounded class and this positive-measure class therefore contain no distinct nontrivial torus pairings to average. Any nontrivial Virasoro boundary ensemble must use genus-one pairings outside these classes, involve additional sectors or vacuum--continuum couplings, or distinguish its members through information not captured by the genus-one pairing. Technically, the proof identifies the Virasoro $S$ and $T$ transformations with the even Weil representation of the metaplectic group and applies the Cowling--Steger lattice-restriction theorem. We also give elementary proofs for several explicit classes of candidate boundary conditions and perform numerical checks of the general result.

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arXiv2026

DualityCert: Verifier-Gated Language-Model Repair of Broken Duality Claims in Quantum Field Theory

We present DualityCert, a symbolic verifier for candidate Seiberg-duality claims in four-dimensional N=1 quiver gauge theories. The verifier evaluates 't Hooft anomaly matching, superpotential R-charge consistency, central-charge matching, and a bounded chiral-ring proxy. A claim that passes receives a consistency certificate, which states that no tested inconsistency was found, not that the duality is proven. We use the verifier as a repair environment for language-model agents, which receive a deliberately broken claim and must edit it until it certifies. On a preregistered benchmark of 145 broken claims, with the analysis fixed before the first confirmatory model call, verifier-gated retry improves final repair success over a single attempt by +8.3 percentage points (pp) on deepseek-chat and +7.1 pp on qwen-plus (Holm-adjusted p<0.002). Under an equal budget of eleven attempts, the stop-first strategy portfolio underperforms independent verifier-filtered resampling by 10.3 percentage points on deepseek-chat but outperforms it by 14.7 points on qwen-plus, reversing the ordering of the two tested verifier-exploitation policies across the two confirmatory models. On qwen-plus, category-level verifier feedback is worth +8.7 pp over content-free retry, and interpretable obligation identities alone are worth +6.4 pp over structurally identical masked feedback. Neither effect is detected on deepseek-chat. Separately, a preregistered MiniMax-M2.5 extension again finds an iteration gain and independent verifier-filtered resampling outperforming the strategy portfolio. Which policy is better thus differs between the two models, while every winning policy uses the same cheap certificate. The verifier, benchmark, protocol, and all per-attempt records are released.

cs.CR↗

arXiv2026

A Crash Course in Supersymmetric Field Theory Across Dimensions

These notes give a cross-dimensional crash course in supersymmetric field theory. The goal is to provide enough common language to recognize the basic setups used in talks and papers, while also working through representative computations that make the terminology concrete. We begin with supersymmetry algebras, multiplets, protected quantities, moduli spaces, deformations, and anomalies, then follow these ideas through examples in two to ten spacetime dimensions. The emphasis is on recurring structures, such as holomorphy, supersymmetric vacua, dualities, extremization principles, indices, BPS data, and anomaly constraints, rather than on a classification of theories in any one dimension.

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arXiv2026

A Linearized Obstruction to the Supersymmetric Extension of Conformal Boundary Conditions in Euclidean Gravity

The conformal boundary condition for gravity fixes the boundary conformal class and the mean curvature, leaving the trace-free extrinsic curvature free as the conjugate response. It is the boundary-value form of York's conformal decomposition of gravitational data, shown to be well posed for Einstein metrics by Anderson. Witten identified it as the elliptic replacement for the ill-posed Dirichlet condition in the finite-boundary perturbative Euclidean gravitational path integral. We show that this perturbative construction admits no half-supersymmetric extension in linearized minimal supergravity. For fixed conformal bosonic data, no half-dimensional gravitino boundary condition (local or pseudodifferential, APS-type included, with any compatible ghost condition at highest-derivative order) closes the full preserved chiral supersymmetry. Supersymmetry first selects the natural local chiral gravitino datum. Acting back on this datum then produces the trace-free extrinsic curvature, precisely the response that the conformal prescription leaves unfixed. The obstruction is therefore not the failure of a particular elliptic ansatz: even the chiral/Robin completion that is LS-elliptic and BRST-compatible at highest-derivative order would impose Dirichlet control on a Neumann response. The obstruction is pointwise in tangential momentum and survives compensating gauge transformations. It is a linearized, highest-derivative obstruction, not a global or nonlinear no-go; nonlinear supercovariant boundary terms may evade it by tying the trace-free extrinsic curvature to gravitino bilinears.

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arXiv2026

Notes on (-2)-form symmetries

We study $(-2)$-form symmetries of a $d$-dimensional quantum field theory, via a $(-1)$-form symmetry of its $(d+1)$-dimensional Symmetry Topological Field Theory (SymTFT), realized by a non-genuine codimension-one defect in the SymTFT bulk attached to a spacetime-filling topological operator. Unlike a $(-1)$-form symmetry of a $d$-dimensional theory, which merely shifts a parameter of the absolute theory, a $(-2)$-form symmetry modifies the SymTFT action, and thereby relates theories whose ordinary global symmetries differ by anomaly data or by the associator data of a non-invertible symmetry. We illustrate the construction in two-dimensional toy models, three-dimensional ABJM-type theories, four-dimensional generalized Yang--Mills theory, and in a fusion-categorical example relating the non-invertible symmetries $\operatorname{Rep}(D_4)$ and $\operatorname{Rep}(Q_8)$. We then develop a club-sandwich realization, in which a quarter-gauging operation interfaces between IR phases of distinct RG flows of a common UV theory, and an alternative realization via nested discrete gauging. Finally, we present a holographic, top-down realization in which the type IIA Romans mass plays the role of a $(-2)$-form background for a three-dimensional Chern--Simons-matter theory, with shifts of the Romans mass realizing shifts of the boundary anomaly coefficients. We also discuss related constructions for coupled bulk--boundary systems.

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arXiv2026

From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs

Building on the viewpoint that ensemble averages in TQFT gravity can be organized by topological boundary data, we develop a SymTFT interpretation of ensemble averaging in low-dimensional holography. The central operation is to keep fixed both the SymTFT and the physical boundary condition, while averaging over topological boundary conditions at the other end of the SymTFT slab. Each such boundary condition gives an absolute completion of the same relative theory, so the ensemble is interpreted as an average over topological completions rather than over arbitrary local dynamics. We formulate this construction in terms of cap functionals and their natural groupoid or Haar-type measures, and illustrate it in two examples. In the closed-string sector of the Marolf--Maxfield model, topological boundary conditions are labelled by finite sets, and the groupoid sum reproduces the Poisson/Bell-polynomial moments. In the Narain case, compact topological boundary conditions of an $\mathbb{R}$-valued BF SymTFT are identified with maximal isotropic subgroups, so that topological-boundary averaging reproduces the usual Narain moduli average with Zamolodchikov measure. We also discuss possible extensions to JT gravity, random matrix theory, Virasoro T(Q)FT, and 3D gravity.

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arXiv2026

Grading the Unspoken: Evaluating Tacit Reasoning in Quantum Field Theory and String Theory with LLMs

Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field theory and string theory. Evaluating this possibility faces an immediate challenge: correctness in these domains is layered, tacit, and fundamentally non-binary. Standard answer-matching metrics fail to capture whether intermediate conceptual steps are properly reconstructed or whether implicit structural constraints are respected. We construct a compact expert-curated dataset of twelve questions spanning core areas of quantum field theory and string theory, and introduce a five-level grading rubric separating statement correctness, key concept awareness, reasoning chain presence, tacit step reconstruction, and enrichment. Evaluating multiple contemporary LLMs, we observe near-ceiling performance on explicit derivations within stable conceptual frames, but systematic degradation when tasks require reconstruction of omitted reasoning steps or reorganization of representations under global consistency constraints. These failures are driven not only by missing intermediate steps, but by an instability in representation selection: models often fail to identify the correct conceptual framing required to resolve implicit tensions. We argue that highly abstract theoretical physics provides a uniquely sensitive lens on the epistemic limits of current evaluation paradigms.

cs.AI↗

arXiv2026

On the SymTFTs of Finite Non-Abelian Symmetries

The $(D+1)$-dimensional symmetry topological field theory (SymTFT$_{D+1}$) of a $D$-dimensional absolute quantum field theory (QFT$_D$) provides a topological characterization of symmetry data. In this framework, the SymTFT comes equipped with a physical boundary specifying a relative QFT, and a topological boundary which specifies the global form of symmetries. In general, there need not be a unique bulk theory which encodes this information but it is often helpful to have a more manifest presentation of symmetries in terms of bulk degrees of freedom. For the case of a finite non-Abelian symmetry group $G$, the bulk SymTFT may be described by a Dijkgraaf-Witten TFT with gauge group $G$. This makes manifest the ``electric'' presentation of the symmetry data but can obscure some of the magnetic data as well as non-Abelian structure present in the absolute QFT$_D$ such as symmetry operators which cannot fully detach from the topological boundary. We address these issues for 3D SymTFTs by constructing discrete BF-like theory Lagrangians for finite groups which admit a presentation as an extension by a finite Abelian group and a finite (possibly non-Abelian) group. This enables us to give a streamlined approach to reconstructing the fusion rules of the accompanying Drinfeld center, but also allows us to construct surface-attaching non-genuine line operators associated directly with non-Abelian group elements rather than just their conjugacy classes. We also sketch how our treatment generalizes to higher-dimensional SymTFTs.

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arXiv2025

SymTFT Entanglement and Holographic (Non)-Factorization

Given two otherwise decoupled $D$-dimensional CFTs which possess a common (finite) symmetry subcategory, one can consider entangled boundary states of their $(D+1)$-dimensional SymTFTs. This roughly corresponds to performing a gauging of the tensor product of two CFTs, and we call this phenomena ``SymTFT entanglement" (or ``S-entanglement" for short). In the case when these CFTs have semiclassical holographic duals, the S-entanglement relates the bulk gauge charges between two otherwise disconnected AdS spacetimes as we highlight in several top-down examples. We show that taking partial traces of such S-entangled states leads to a streamlined approach to preparing ensemble-averaged CFTs in string theory. This ensemble averaging coincides with that generated by $\alpha$-states in the baby universe Hilbert space, and we propose a symmetry-enriched generalization of this Hilbert space via generalized global symmetries. We quantify how this symmetry-governed averaging violates holographic factorization and leads to the emergence of bulk global symmetries. We also consider the eternal (two-sided) AdS black hole geometries, where our SymTFT entanglement considerations imply that there exist refinements of the usual theromofield double state preparation of the system. We show that one may prepare the system in such a way that the total CFT data does not factorize into left and right copies. As anticipated by Marolf and Wall \cite{Marolf:2012xe}, we highlight that such considerations are necessary to define the gauge charges of eternal black holes, and in certain cases, can imply that there exist extended bulk objects stretching across the wormhole which cannot be expressed in terms of a product of left and right CFT operators.

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arXiv2025

Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries

In this note we consider examples of decomposition (in which a local QFT is equivalent to a disjoint union of multiple independent theories, known as universes) where there is a continuous familiy of universes, rather than a finite or countably infinite collection. In particular, this allows us to consistently eliminate all instantons in a local QFT via a suitable topological gauging of the (-1)-form symmetry. In two-dimensional U(1) gauge theories, this is equivalent to changing the gauge group to R. This makes both locality as well as the instanton restriction explicit. We apply this to clarify the Gross-Taylor string interpretation of the decomposition of two-dimensional pure Yang-Mills. We also apply decomposition to study two-dimensional R gauge theories, such as the pure R Maxwell theory, and two-dimensional supersymmetric gauged linear sigma models whose gauge groups have factors of R. In that context, we find that analogues of the Witten effect for dyons, here rotating between universes, play a role in relating anomalies of the individual universes to (different) anomalies in the disjoint union. Finally, we discuss limits of the Tanizaki-Unsal construction, which accomplish instanton restriction by topologically gauging a Q/Z (-1)-form symmetry, and speculate in two-dimensional theories on possible interpretations of those limits in terms of the adelic solenoid.

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arXiv2025

On mixed 't Hooft anomalies of emergent symmetries

In this paper, we investigate the dynamical constraints imposed on the UV theory when it develops an emergent symmetry in the infrared with mixed 't Hooft anomalies. We demonstrate that, under certain conditions, the UV theory must contain non-genuine operators. Our primary examples illustrating this phenomenon are 2D gauged linear sigma models and 3D Chern-Simons-matter theories. Through this analysis, we establish connections between different classes of topological quantum field theories and propose a correspondence between quantum cohomologies of distinct target spaces.

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arXiv2025

von Neumann Subfactors and Non-invertible Symmetries

We use the language of von Neumann subfactors to investigate non-invertible symmetries in two dimensions. A fusion categorical symmetry $\mathcal{C}$, its module category $\mathcal{M}$, and a gauging labeled by an algebra object $\mathcal{A}$ are encoded in the bipartite principal graph of a subfactor. The dual principal graph captures the quantum symmetry $\mathcal{C}'$ obtained by gauging $\mathcal{A}$ in $\mathcal{C}$, as well as a reverse gauging back to $\mathcal{C}$. From a given subfactor $N \subset M$, we derive a quiver diagram that encodes the representations of the associated non-invertible symmetry. We show how this framework provides necessary conditions for admissible gaugings, enabling the construction of generalized orbifold groupoids. To illustrate this strategy, we present three examples: Rep$(D_4)$ as a warm-up, the higher-multiplicity case Rep$(A_4)$ with its associated generalized orbifold groupoid and triality symmetry, and Rep$(A_5)$, where $A_5$ is the smallest non-solvable finite group. For applications to gapless systems, we embed these generalized gaugings as global manipulations on the conformal manifolds of $c=1$ CFTs and uncover new self-dualities in the exceptional $SU(2)_1/A_5$ theory. For $\mathcal{C}$-symmetric TQFTs, we use the subfactor-derived quiver diagrams to characterize gapped phases, describe their vacuum structure, and classify the recently proposed particle-soliton degeneracies.

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arXiv2024

Gauging in Parameter Space: A Top-Down Perspective

In this paper, we discuss a novel top-down perspective on gauging parameters in quantum field theories (QFTs) by promoting them to partially dynamical fields. Through a generalized notion of symmetry theories, we explore the consequences of this promotion, revealing new topological defects, decompositions as well as generalized symmetry structures across various dimensions. We provide a systematic top-down derivation of symmetry theories for parameters and discuss how special types of branes, such as Euclidean branes and fluxbranes are related to gauging in the parameter space in QFTs. We illustrate our theoretical framework with two key examples: the modified instanton sum in 4D $\mathcal{N}=4$ super Yang-Mills theory and the gauging of gauge ranks in 3D ABJ(M) theories.

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arXiv2024

Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases

In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions, extending our previous work. Specifically, in this work we discuss more general gauged noninvertible symmetries in which the noninvertible symmetry is not multiplicity free, and discuss the case of Rep$(A_4)$ in detail. We realize Rep$(A_4)$ gaugings for the $c = 1$ CFT at the exceptional point in the moduli space and find new self-duality under gauging a certain non-group algebra object, leading to a larger noninvertible symmetry Rep$(SL(2, Z_3))$. We also discuss more general examples of decomposition in two-dimensional gauge theories with trivially-acting gauged noninvertible symmetries.

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arXiv2024

Chern-Simons theory, decomposition, and the A model

In this paper, we discuss how gauging one-form symmetries in Chern-Simons theories is implemented in an A-twisted topological open string theory. For example, the contribution from a fixed H/Z bundle on a three-manifold M, arising in a BZ gauging of H Chern-Simons, for Z a finite subgroup of the center of H, is described by an open string worldsheet theory whose bulk is a sigma model with target a Z-gerbe (a bundle of one-form symmetries) over T^* M, of characteristic class determined by the H/Z bundle. We give a worldsheet picture of the decomposition of one-form-symmetry-gauged Chern-Simons in three dimensinos, and we describe how a target-space constraint on bundles arising in the gauged Chern-Simons theory has a natural worldsheet realization. Our proposal provides examples of the expected correspondence between worldsheet global higher-form symmetries, and target-space gauged higher-form symmetries.

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arXiv2024

Generalized Symmetries in 2D from String Theory: SymTFTs, Intrinsic Relativeness, and Anomalies of Non-invertible Symmetries

Generalized global symmetries, in particular non-invertible and categorical symmetries, have become a focal point in the recent study of quantum field theory (QFT). In this paper, we investigate aspects of symmetry topological field theories (SymTFTs) and anomalies of non-invertible symmetries for 2D QFTs from a string theory perspective. Our primary focus is on an infinite class of 2D QFTs engineered on D1-branes probing toric Calabi-Yau 4-fold singularities. We derive 3D SymTFTs from the topological sector of IIB supergravity and discuss the resulting 2D QFTs, which can be intrinsically relative or absolute. For intrinsically relative QFTs, we propose a sufficient condition for them to exist. For absolute QFTs, we show that they exhibit non-invertible symmetries with an elegant brane origin. Furthermore, we find that these non-invertible symmetries can suffer from anomalies, which we discuss from a top-down perspective. Explicit examples are provided, including theories for $Y^{(p,k)}(\mathbb{P}^2)$, $Y^{(2,0)}(\mathbb{P}^1\times \mathbb{P}^1)$, and $\mathbb{C}^4/\mathbb{Z}_4$ geometries.

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arXiv2023

Non-invertible Symmetries in 2D from Type IIB String Theory

We propose a top-down approach to non-invertible symmetries in 2D QFTs and their associated symmetry topological field theories. We focus on the gauge theory engineered on D1-branes probing a particular Calabi-Yau 4-fold singularity. We show how to derive the symmetry topological field theory, a 3D Dijkgraaf-Witten theory, from the IIB supergravity under dimensional reduction. We also identify branes behind the non-invertible topological lines by dimensionally reducing their worldvolume actions. The action of non-invertible lines on charged local operators is then realized as the Hanany-Witten transition.

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