arXiv subjects

Hao Y. Zhang

Publications and source records attributed to Hao Y. Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Perturbative Anomaly Inflow on Orbifolds

We study perturbative anomaly inflow for effective theories supported on orbifold fixed loci of the internal geometry. Donnelly's equivariant APS theorem gives a fixed-point density, whose degree-$(d+2)$ component is identified as the anomaly polynomial of the $d$-dimensional effective theory. We apply the construction to six-dimensional A-type orbi-instanton theories engineered by $N$ M5-branes probing a transverse $\mathbb{C}^2/\mathbb{Z}_k$ singularity at an end-of-the-world M9-brane. For a flat $E_8$ connection specified by $ρ:\mathbb{Z}_k\to E_8$, we compute the non-identity ALE fixed-point class on the M9 wall. Its degree-eight component agrees with the complete Kac-label-dependent remainder conjectured in \cite{MOTZ} by Mekareeya-Ohmori-Tachikawa-Zafrir, including the $SU(2)_R$ and tangent-bundle curvatures. Together with the known M5/Hořava--Witten and ALE/Hořava--Witten terms, this reproduces the unflavored tensor-branch anomaly polynomial. This local equality further suggests a complete M-theory corner-inflow interpretation. The same prescription also be extended to include flavor symmetries as the centralizer of $E_8$.

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arXiv2026

Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D

We investigate the landscape of 6d $\mathcal{N}=(1,0)$ D-type orbi-instanton superconformal field theories (SCFTs) and their torus compactifications to four-dimensional class $\mathcal{S}$ theories. By analysing a general class of 6d F-theory constructions via generalised quivers, we demonstrate that -- in contrast to the well-characterised A-type series -- the dimensional reductions that admit a 4d class $\mathcal{S}$ description on a Riemann sphere with three untwisted D-type punctures constitute only a subset of the full orbi-instanton landscape. For this subclass, we show that the punctures can be effectively characterised by two sets of integers: the $s$-labels and the $m$-labels. The $s$-labels, or ``Kac-type labels'', serve as the D-type analogues to the Kac labels used in A-type theories; we establish their correspondence with ``modified excess numbers'' in the associated 3d mirror theories (magnetic quivers). The $m$-labels are further introduced to streamline the mapping from 6d generalised quivers to their class $\mathcal{S}$ descriptions. Furthermore, we analyse physical distinctions arising from 6d $θ$ angles and explore the hierarchy of Higgs branch flows. In doing so, we uncover instances of ``hidden Higgsings'' -- renormalization group flows present in the 6d parent theories that are not manifest in the puncture closures of the corresponding class $\mathcal{S}$ descriptions.

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arXiv2026

Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions

We generalize the framework of spurion analysis to a class of selection rules arising from non-invertible fusion algebras in perturbation theory. As a first step toward systematic applications to particle physics, we analyze the near-group fusion algebras, defined by fusion rules built from a finite Abelian group $G$ extended by a single non-invertible element. Notable examples include the Fibonacci and Ising fusion rules. We introduce a systematic scheme for labeling coupling constants at the level of the non-invertible fusion algebra, enabling consistent tracking of couplings when constructing composite amplitudes from simpler building blocks. Our labeling provides a clear interpretation of why the tree-level exact non-invertible selection rules are violated through radiative corrections, a unique phenomenon essential to ``loop-induced groupification''. We also identify the limit where the near-group fusion algebra is lifted to a $G\times \mathbb{Z}_2$ group, which provides an alternative scheme of spurion analysis consistent with the original one based on the near-group algebra. Meanwhile, we highlight the distinctions between the selection rules imposed by the near-group fusion algebra and those from breaking the $G\times \mathbb{Z}_2$ group.

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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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arXiv2026

K-theoretic Global Symmetry in String-constructed QFT and T-duality

We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have \textit{even-form} and \textit{odd-form} symmetries determined by $K_N(\partial X)$, the twisted K-theory as D-brane charges on the asymptotic boundary $\partial X$ of internal geometry $X$ with twist class $N$. For these QFTs, ``\textit{$p$-form symmetries}" are no longer separately well-defined for individual $p$, but are instead mixed together. We discuss 6D ADE-type (2,0) SCFTs and some 6d (1,0) LSTs as examples and demonstrate their twisted K-theoretic symmetries, and we checked them to be compatible with T-duality. We further point out, through explicit examples, that K-theory leads to symmetry extensions that cannot be detected by cohomology for Type II string theory on certain orbifolds of $\mathbb{C}^3$ and $\mathbb{C}^4$. We also discuss the implications of these results in the dual brane descriptions.

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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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arXiv2025

On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories

We show that the low-energy effective actions of two ten-dimensional supersymmetric heterotic strings are different by a $\mathbb{Z}_3$-valued discrete topological term even after we turn off the $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$ gauge fields. This will be demonstrated by considering the inflow of normal bundle anomaly to the respective NS5-branes from the bulk. We also find that the $Spin(16)\times Spin(16)$ non-tachyonic non-supersymmetric heterotic string has the same non-zero $\mathbb{Z}_3$-valued discrete topological term. We will also explain the relation of our findings to the theory of topological modular forms. The paper is written as a string theory paper, except for an appendix translating the content in mathematical terms. We will explain there that our finding identifies a representative of the $\mathbb{Z}/3$-torsion element of $π_{-32}\mathrm{TMF}$ as a particular self-dual vertex operator superalgebra of $c=16$ and how we utilize string duality to arrive at this statement.

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arXiv2025

Type I anomaly cancellation revisited

We revisit the issue of how the perturbative and global fermion anomaly of Type I string theory in ten dimensions is cancelled by the Green-Schwarz mechanism using the RR fields. This will be done by realising the RR fields as boundary modes of an eleven-dimensional bulk theory described in terms of a quadratic refinement of the differential KO-theory pairing. We will then generalise this analysis to Sugimoto's $usp(32)$ string and Sagnotti's $u(32)$ string. We also discuss in a more general setting the procedures which need to be followed when we try to cancel fermion anomalies in terms of $p$-form fields based on differential K-theory classes. This we illustrate by performing an analysis of the mod-2 anomaly cancellation in nine dimensions arising from the $S^1$ compactification of the Type I theory.

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arXiv2025

Atomic Higgsings of 6D SCFTs

In this paper, we study the full Higgs branch Hasse diagram for any given 6d $\mathcal{N}=(1,0)$ SCFT constructed via F-theory. This can be done by a procedure of determining all the minimal Higgsings on the generalized quiver of the 6d SCFT. We call this procedure the atomic Higgsing, which can be implemented iteratively. We present our general algorithms with many concrete examples of Hasse diagrams. We also compare our algorithm with the Higgsings determined by the 3d $\mathcal{N} = 4$ magnetic quivers. For the cases where the magnetic quivers are unitary, we can reproduce the full Hasse diagrams. We also construct the orthosymplectic magnetic quivers from the Type IIA brane systems for some new examples. Our approach, based on F-theory, applies to the known and new orthosymplectic cases, as well as theories that do not have known descriptions in terms of magnetic quivers. We expect our geometry-based approach to help extend the horizon of the RG flows of the 6d SCFTs.

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arXiv2025

Atomic Higgsings of 6D SCFTs II: Induced Flows

We study a specific type of atomic Higgsings of the 6d $\mathcal{N}=(1,0)$ theories, which we call the induced flows. For the conformal matter theory associated with a pair of nilpotent orbits, the induced flows are given by the inductions of the orbits. We also consider the induced flows for the orbi-instanton theories (as well as some little string theories) that are associated with the homomorphisms from the discrete subgroups of $\mathrm{SU}(2)$ to $E_8$. This gives a physical definition of the inductions among these discrete homomorphisms, analogous to the inductions of the nilpotent orbits. We analyze the Higgs branch dimensions, the monotonicity of the Weyl anomalies (or the 2-group structure constants for LSTs) and the brane pictures under the induced flows.

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arXiv2024

Frozen Generalized Symmetries

M-theory frozen singularities are (locally) $D$- or $E$-type orbifold singularities with a background fractional $C_3$-monodromy surrounding them. In this paper, we revisit such backgrounds and address several puzzling features of their physics. We first give a top-down derivation of how the $D$- or $E$-type 7D $\mathcal{N}=1$ gauge theory directly ``freezes" to a lower rank gauge theory due to the $C_3$-background. This relies on a Hanany--Witten effect of fractional M5 branes and the presence of a gauge anomaly of fractional D$p$ probes in the circle reduction. Additionally, we compute defect groups and 8D symmetry topological field theories (SymTFTs) of the 7D frozen theories in several duality frames. We apply our results to understanding the evenness condition of strings ending on $O7^+$-planes, and calculating the global forms of supergravity gauge groups of M-theory compactified on $T^4/Γ$ with frozen singularities. In an Appendix, we also revisit IIA $ADE$ singularities with a $C_1$-monodromy along a 1-cycle in the boundary lens space and show that this freezes the gauge degrees-of-freedom via confinement.

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arXiv2024

Top Down Approach to Topological Duality Defects

Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D $\mathcal{N} = 4$ Super Yang-Mills (SYM) theory, an appropriate choice of (complexified) gauge coupling and global form of the gauge group can lead to a rather rich fusion algebra for the associated defects, leading to examples of non-invertible symmetries. In this work we present a top down construction of these duality defects which generalizes to QFTs with lower supersymmetry, where other 0-form symmetries are often present. We realize the QFTs of interest via D3-branes probing $X$ a Calabi-Yau threefold cone with an isolated singularity at the tip of the cone. The IIB duality group descends to dualities of the 4D worldvolume theory. Non-trivial codimension one topological interfaces arise from configurations of 7-branes "at infinity" which implement a suitable $SL(2, \mathbb{Z})$ transformation when they are crossed. Reduction on the boundary topology $\partial X$ results in a 5D symmetry TFT. Different realizations of duality defects, such as the gauging of 1-form symmetries with certain mixed anomalies and half-space gauging constructions, simply amount to distinct choices of where to place the branch cuts in the 5D bulk.

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arXiv2024

On a class of selection rules without group actions in field theory and string theory

We discuss a class of selection rules which i) do not come from group actions on fields, ii) are exact at tree level in perturbation theory, iii) are increasingly violated as the loop order is raised, and iv) eventually reduce to selection rules associated with an ordinary group symmetry. We start from basic field-theoretical examples in which fields are labeled by conjugacy classes rather than representations of a group, and discuss generalizations using fusion algebras or hypergroups. We also discuss how such selection rules arise naturally in string theory, such as for non-Abelian orbifolds or other cases with non-invertible worldsheet symmetries.

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arXiv2023

The Branes Behind Generalized Symmetry Operators

The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry $X$, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary $\partial X$. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in $\partial X$. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

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arXiv2023

Intermediate Defect Groups, Polarization Pairs, and Non-invertible Duality Defects

Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing non-invertible duality defects in theories in $2k$ spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their $(k-1)$-form defect groups are concerned, including their $(k-1)$-form symmetries, global structures (including discrete $θ$-angle), and local counterterms. Using the associated symmetry TFT, we show that the polarization pair is capable of succinctly describing topological manipulations, e.g., gauging $(k-1)$-form global symmetries and stacking counterterms, of absolute QFTs. Furthermore, automorphisms of the $(k-1)$-form charge lattice naturally act on polarization pairs via their action on the defect group; they can be viewed as dualities between absolute QFTs descending from the same relative QFT. Using this formalism, we present a prescription for building non-invertible symmetries of absolute QFTs. A large class of known examples, e.g., non-invertible defects in 4D $\mathcal{N}=4$ super-Yang--Mills, can be reformulated via this prescription. As another class of examples, we identify and investigate in detail a family of non-invertible duality defects in 6D superconformal field theories (SCFTs), including from the perspective of the symmetry TFT derived from Type IIB string theory.

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arXiv2023

Generalized Symmetries in Supergravities and Superconformal Field Theories via String Theory

In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions. Answering this question requires us to combine the following two approaches. In the "top-down" approach, We focus on supergravity theories in 7, 8, and 9 dimensional spacetime with 16 supercharges. We emphasize two discrete aspects of these theories: generalized global symmetries and frozen singularities. We give an exhaustive classification of IIB supergravity theory in 8D, particularly emphasizing these two discrete aspects. In the "bottom-up" approach, we present a consistency condition of general 8D supergravity theories involving their higher-form symmetries use it to rule out many global structures of the gauge groups in 8D supergravity theories that do not admit string theory constructions. Part two studies the generalized global symmetries of geometrically-engineered quantum field theories via string theory. We examined branes wrapping on relative topological cycles that give heavy defects that are charged under generalized global symmetries, which can then be used to construct new lower-dimensional theories. By investigating the string theory origin of the topological operators, we provide a general construction of these topological operators in the context of geometric engineering as branes wrapped on the homological cycles in the asymptotic boundary of the internal geometry. We illustrate this proposal by determining non-invertible 2-form symmetries in 6D superconformal field theories. Furthermore, by wrapping type IIB 7-brane on the entire asymptotic boundary of the internal manifold, we explicitly give a unified string-theoretic construction of two different types of field-theoretic non-invertible duality defects.

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arXiv2022

6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6d gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible non-trivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4d $\mathcal{N} = 2$ SCFTs obtained by compactifying on a $T^2$ in the presence of a topologically non-trivial flat flavor bundle characterized by a 't Hooft magnetic flux. The resulting "Stiefel--Whitney twisted" compactifications realize several new infinite families of 4d $\mathcal{N} = 2$ SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d $\mathcal{N} = 2$ SCFTs.

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arXiv2022

Higher Symmetries of 5d Orbifold SCFTs

We determine the higher symmetries of 5d SCFTs engineered from M-theory on a $\mathbb{C}^3 / Γ$ background for $Γ$ a finite subgroup of $SU(3)$. This resolves a longstanding question as to how to extract this data when the resulting singularity is non-toric (when $Γ$ is non-abelian) and/or not isolated (when the action of $Γ$ has fixed loci). The BPS states of the theory are encoded in a 1d quiver quantum mechanics gauge theory which determines the possible 1-form and 2-form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0-form symmetry, the abelianization of $Γ$ detects a 2-group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.

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