arXiv subjects

Qiang Jia

Publications and source records attributed to Qiang Jia.

At least 19 recordsLinked to original sources

arXiv2026

On general background of quantum non-invertible symmetry in 2D

We study the dual quantum symmetry $\mathrm{Rep}(G)$ in the two-dimensional theory $\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$ obtained by gauging a non-abelian symmetry $G$ of $\mathfrak{T}_G$, where for Lie groups $G$ the gauging is understood as flat gauging. We develop a general framework for computing partition functions of $\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$ in arbitrary non-invertible symmetry backgrounds, represented by topological defect networks of $\mathrm{Rep}(G)$, in terms of the partition functions of the original theory $\mathfrak{T}_G$. We also derive the inverse transformation, expressing partition functions of $\mathfrak{T}_G$ in $G$ backgrounds in terms of those of $\widetilde{\mathfrak{T}}_{\mathrm{Rep}(G)}$. We test the framework in several examples, including finite groups with multiplicity-free and higher-multiplicity fusion rules, and discuss a formal extension to compact Lie groups, focusing on $\mathrm{Rep}(SU(2))$.

hep-th↗

arXiv2026

Flat Gauging of Continuous (Non-invertible) Symmetries and Non-compact BF SymTFT for Compact Boson

We study flat gauging of continuous symmetries by summing over flat gauge-field configurations. We focus on the two-dimensional compact boson and construct the torus partition function with general flat $U(1)_M\times U(1)_W$ backgrounds. We show that flat gauging either $U(1)_M$ or $U(1)_W$ decompactifies the theory to the non-compact free boson, and that the dual $\mathbb{Z}$ background combines with the remaining $U(1)$ background into a non-compact $\mathbb{R}$ symmetry background due to the mixed anomaly. We also revisit the self-dual radius, where flat gauging the diagonal $SO(3)\subset (SU(2)_L\times SU(2)_R)/\mathbb{Z}_2$, first pointed out by Gaberdiel and Suchanek, gives the continuous orbifold which lies outside the usual $c=1$ moduli space. On the orbifold branch, we study finite and continuous non-invertible flat gaugings and explain why the continuous case requires a prescription for zero-measure fixed loci on the moduli space. Finally, we formulate the SymTFT of torus sigma models as a non-compact BF theory, whose topological boundary states encode the Narain moduli space and the $O(D,D;\mathbb{Z})$ T-duality action.

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arXiv2026

Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries

We present a quantum mechanical approach to understanding the Hilbert space and the defect Hilbert spaces associated with line operators of BF theory combined with level-$k$ Chern-Simons theory. The defect Hilbert spaces are closely related to the category of $*$-representations of the $C^*$-algebra of the compactly supported sections of the Fell line bundle over the conjugation action groupoid $G//_{\mathrm Ad} G$, and the structure of this category and the groupoid action on the objects of this category is interpreted quantum mechanically. We show that the action of the line operators on the Hilbert space of the $BF+kCS$ TQFT is given concretely by a convolution between the kernels that represent the line operators, and that the codimension-$2$ twist and the codimension-$1$ prequantum line bundle arise as two transgressions of the same universal level $k\in H^4(BG,\mathbb{Z})$. For finite gauge group, the resulting convolution-eigenvalue formula is identified with the Verlinde formula for the (twisted) Drinfeld double $D^\omega(G)$ via an explicit phase-by-phase match with the known finite modular data. For compact Lie group, the convolution-kernel eigenvalues coincide in the regular sector with the semiclassical Hopf-link $S$-kernel, identifying two complementary derivations of the same modular data.

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arXiv2026

Candidate Gaugings of Categorical Continuous Symmetry

Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a symmetry category $\mathscr{C}^k(G)$ associated to a QFT with continuous global $G$-symmetry and possible 't Hooft anomaly labeled by an integer $k$. We use the combination of the $BF$ theory and the level-$k$ Chern-Simons theory with gauge group $G$ as a semiclassical kernel-theoretic model for the corresponding SymTFT. Under two explicit assumptions, namely that this $BF{+}k$CS theory provides the relevant SymTFT model and that the common $+1$ eigenspaces of the resulting modular kernels detect candidate Lagrangian algebra data in the continuous setting, we derive candidate modular $S$- and $T$-kernels from Hopf-link and framing correlators in $S^3$ semi-classically. We then use these kernels to obtain candidate modular invariants and candidate gaugings. The resulting formulas recover the established cases and suggest a possible extension of this kernel-theoretic picture to compact Lie groups.

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arXiv2026

Categorical Symmetries via Operator Algebras

We propose that the symmetry category associated to a 2D quantum field theory with 0-form $G$-symmetry with 't Hooft anomaly $k\in H^4(BG,\mathbb{Z})$ for a large class of Lie groups $G$ is the category of twisted measurable fields of Hilbert spaces over $G$ denoted by $\mathrm{Hilb}^k(G)$, which is equivalent to the category of unitary representations of $C_0(G)$ with convolution product twisted by a multiplicative bundle gerbe labeled by $k$ denoted by $\textbf{Rep}^k(C_0(G))$. We find that the Drinfeld center of the symmetry category $\mathcal{Z}(\mathrm{Hilb}^{k}(G))$ equivalent to the category of unitary representations of the groupoid $C^*$-algebra of the Fell line bundle $\Sigma_k$ over the conjugation action groupoid $G//_{\rm Ad} G$, denoted by $\textbf{Rep}(C^*(G//_{\rm Ad}G,\Sigma_k))$, where the twist is characterized by the transgression $\tau(k)\in H^2(G//_{\rm Ad}G,U(1))$. To the full generality, our framework applies to a Lie group $G$ that is a direct product of a compact connected Lie group and a number of $\mathbb{R}$ or $GL(1,\mathbb{C})$ factors. We compute the braiding of anyon lines in the bulk 3D SymTFT from this formalism. Finally we provide physical examples for abelian and non-abelian $G$, and discuss the physical consequences of flat gauging continuous global symmetries.

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arXiv2025

Fermionic Non-invertible Symmetry Behind Supersymmetric ADE Solitons

The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the categorical symmetry data in a massive fermionic model. The algebra and its representations explicitly encode the vacuum structure, soliton degeneracies, and their quantum numbers. As a demonstration, we apply this framework to the $\mathcal N=2$ minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of $\text{SU}(2)_k$ known to underlie the $ADE$ classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting $ADE$-type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems.

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arXiv2025

Anomaly of Continuous Symmetries from Topological Defect Network

We show that the 't Hooft anomaly of a quantum field theory with continuous flavor symmetry can be detected from rearrangements of the topological defect webs implementing the global symmetry in general spacetime dimension, which is concretized in 2D by the F-moves of the defect lines. Via dualizing the defects to flat background gauge field configurations, we characterize the 't Hooft anomaly by various cohomological data of the symmetry group, where the cohomology of Lie groups with discrete topology plays the central role. We find that an extra dimension emerges naturally as a consequence of the mathematical description of the 't Hooft anomaly in the case of flat gauging.

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arXiv2025

Categorical Continuous Symmetry

We define the symmetry category in 1+1d for continuous 0-form $G$-symmetry to be $\textbf{Sky}^\tau(G)$, the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of $G$, where $\tau \in H^4(BG,\mathbb{Z})$ is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of $\textbf{Sky}^\tau(G)$. We show explicitly the way that $\tau$ twists the convolution tensor product of the objects of $\textbf{Sky}^\tau(G)$. As a concrete example, we present the $S$ and $T$-matrices for the simple anyons of the resulting $Z(\textbf{Sky}^\tau(G))$ category for $G = U(1)$, both for the cases without or with anomaly and discuss the topological boundary conditions as Lagrangian algebra of $Z(\textbf{Sky}^{\tau}(U(1)))$. We also present the definition of $\textbf{Sky}^\tau(G)$ and $Z(\textbf{Sky}^\tau(G))$ for the non-abelian case of $G=SU(2)$, as well as the speculated modular data. We point out that in order to have a physically relevant center and Lagrangian algebras it is necessary to generalize $\textbf{Sky}^\tau(G)$ to a larger category, which we argue to be closely related to the category of quasi-coherent sheaves on $G_\mathbb{C}$ with convolution tensor product twisted by $\tau$.

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arXiv2025

Symmetry, Symmetry Topological Field Theory and von Neumann Algebra

We study the additivity and Haag duality of the von Neumann algebra of a quantum field theory $\mathcal{T}_\mathcal{F}$ with 0-form (and the dual $(d-2)$-form) (non)-invertible global symmetry $\mathcal{F}$. We analyze the symmetric (uncharged) sector von Neumann algebra of $\mathcal{T}_\mathcal{F}$ with the inclusion of bi-local and bi-twist operators in it. We establish the connection between the existence of these non-local operators in $\mathcal{T}_\mathcal{F}$ and certain properties of the Lagrangian algebra $\mathcal{L}$ of the extended operators in the corresponding symmetry topological field theory (SymTFT). We prove that additivity or Haag duality of the symmetric sector von Neumann algebra is violated when $\mathcal{L}$ satisfies specific criteria, thus generalizing the result of Shao, Sorce and Srivastava to arbitrary dimensions. We further demonstrate the SymTFT construction via concrete examples in two dimensions.

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arXiv2025

Classification of monopole deformed 3d $\mathcal{N}=2$ Seiberg-like duality with an adjoint matter

We propose a new 3d $\mathcal{N}=2$ Seiberg-like duality of adjoint SQCD(Kim-Park duality) with linear monopole superpotential terms which encompasses known monopole deformed Kim-Park dualities. Equipped with this, we classify all the monopole deformed Kim--Park dualities up to quadratic powers of monopole deformations, and find all are equivalent either to the original Kim--Park, or to the proposed duality. With the recently developed deconfined perspective, this means all the working monopole deformed Kim--Park dualities up to quadratic terms are assembled by the Aharony and Benini-Benvenuti-Pasquetti dualities.

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arXiv2025

Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory

Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to subsystem symmetries and develop subsystem SymTFT as a systematic tool to characterize and classify subsystem symmetry-protected topological (SSPT) phases. For $(2+1)$D gapped phases, we introduce a 2-foliated $(3+1)$D exotic tensor gauge theory (which is equivalent to 2-foliated $(3+1)$D BF theory via exotic duality) as the subsystem SymTFT and systematically analyze its topological boundary conditions and linearly rigid subsystem symmetries. Taking subsystem symmetry groups $G = \mathbb{Z}_N$ and $G=\mathbb{Z}_N \times \mathbb{Z}_M$ as examples, we demonstrate how to recover the classification scheme $\mathcal{C}[G] = H^{2}(G^{\times 2}, U(1)) / \left( H^2(G, U(1)) \right)^3$, which was previously derived by examining topological invariant under linear subsystem-symmetric local unitary transformations in the lattice Hamiltonian formalism. To illustrate the correspondence between field-theoretic and lattice descriptions, we further analyze $\mathbb{Z}_2 \times \mathbb{Z}_2$ and $\mathbb{Z}_N \times \mathbb{Z}_M$ cluster state models as concrete examples.

cond-mat.str-el↗

arXiv2025

Symmetry Topological Field Theory for Flavor Symmetry

In this Letter, we demonstrate that the Symmetry Topological Field Theory (SymTFT) associated to a Quantum Field Theory (QFT) with continuous non-abelian $G$-flavor symmetry is a $BF$-theory with gauge group $G$. We show that gauging $G$-symmetry with a flat connection yields a theory with global symmetry characterized by exchanging the conjugate variables in the quantization of $BF$-theory. We construct the extended operators that generate the $G$-flavor symmetry and the $(d-2)$-form $\text{Rep}(G)$-symmetry of the gauged QFT. We demonstrate that $BF$-theory arises as the theory characterizing $G$-flavor symmetry of a QFT in the AdS/CFT setup. 't Hooft anomalies of the $G$-flavor symmetry are realized as extra terms in the action.

hep-th↗

arXiv2025

From BPS Spectra of Argyres-Douglas Theories to Families of 3d TFTs

Vertex operator algebras (VOAs) arise in protected subsectors of supersymmetric quantum field theories, notably in 4d ${\mathcal N}=2$ superconformal field theories (SCFT) via the Schur sector and in twisted 3d ${\mathcal N}=4$ theories via boundary algebras. These constructions are connected through twisted circle compactifications, which can be best understood from the dynamics of BPS particles in the Coulomb branch of the 4d SCFT. This data is encoded in an operator $\hat\Phi$ acting on the Hilbert space of an auxiliary quantum mechanics of BPS particles, whose trace yields the partition functions of a 3d topological field theory (TFT) bounding the VOA. We generalize this trace formula by considering higher powers of $\hat\Phi$, leading to a finite family of VOAs associated with a given 4d SCFT. Applying this framework to Argyres-Douglas theories labeled by $(A_1, G)$, where $G$ is an ADE-type group of rank up to 8, we extract the modular data of the family of boundary VOAs via TFT partition function calculations on Seifert manifolds. Our results suggest that the modular data obtained from different powers of $\hat\Phi$ are related by Galois transformations.

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arXiv2024

SymTFT Approach to 2D Orbifold Groupoids: `t Hooft Anomalies, Gauging, and Partition Functions

We use the 3D SymTFT approach to study the generalized symmetries and partition functions of 2D CFTs in various orbifolded and fermionic phases. These phases can be realized by the sandwich construction in the associated 3D SymTFTs with different gaped boundaries that encode the data of symmetries in the 2D CFTs. We demonstrate that the gaped boundaries can all be identified with the (fermionic) Lagrangian algebra in the 3D SymTFT, and thus use them to establish webs of dualities of the boundary CFTs in different phases on the level of partition functions. In addition, we introduce the concept of ``para-fermionic Lagrangian algebra" which enables us to construct the partition functions of para-fermionized CFTs on the 2D boundary. Finally, we provide many important examples, including a 3D SymTFT viewpoint on gauging non-invertible symmetries in 2D CFTs.

hep-th↗

arXiv2024

Web of 4D Dualities, Supersymmetric Partition functions and SymTFT

We study $\mathbb{Z}_N$ one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its canonical quantization and construct topological boundary states on several important classes of four manifolds that are spin, non-spin and torsional. We highlight a web of four-dimensional dualities, which can be naturally interpreted within the SymTFT framework. We also point out an intriguing class of four-dimensional gauge theories that exhibit mixed 't Hooft anomaly between one-form symmetries. In the second part of this work, we extend the SymTFT to account for various quantities protected by supersymmetry (SUSY) in SUSY gauge theories. We proposed that their behaviour under various symmetry operations are entirely captured by the topological boundary of the SymTFT, resulting in strong constraints. Concrete examples are considered, including the Witten index, the lens space index and the Donaldson-Witten and Vafa-Witten partition functions.

hep-th↗

arXiv2024

Discrete Gauge Anomalies and Instantons

We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague $d=4$ $Sp(k)$ theories, is well-understood in terms of $π_4(Sp(k))=\mathbb{Z}_2$, but it also has an oblique relation to the instantons, labeled by $π_3(G)=\mathbb{Z}$, via the fermion zero mode counting. We revisit this relation and point out how $SU(N)$ theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in $d=3$.

hep-th↗

arXiv2024

Symmetry TFT for Subsystem Symmetry

We generalize the idea of symmetry topological field theory (SymTFT) for subsystem symmetry. We propose the 2-foliated BF theory with level $N$ in $(3+1)$d as subsystem SymTFT for subsystem $\mathbb Z_N$ symmetry in $(2+1)$d. Focusing on $N=2$, we investigate various topological boundaries. The subsystem Kramers-Wannier and Jordan-Wigner dualities can be viewed as boundary transformations of the subsystem SymTFT and are included in a larger duality web from the subsystem $SL(2,\mathbb Z_2)$ symmetry of the bulk foliated BF theory. Finally, we construct the condensation defects and twist defects of $S$-transformation in the subsystem $SL(2,\mathbb Z_2)$, from which the fusion rule of subsystem non-invertible operators can be recovered.

hep-th↗

arXiv2023

$\mathbb{Z}_N$ Duality and Parafermions Revisited

Given a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level $2$. From a Hamiltonian perspective, the information of dualities is encoded in a topological boundary state which is defined as an eigenstate of certain Wilson loop operators (anyons) in the bulk. We generalize this story to two-dimensional theories with non-anomalous $\mathbb{Z}_N$ symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with $\mathbb{Z}_N$ or subgroups of $\mathbb{Z}_N$, and discuss their algebraic properties as well as the $\mathbb{Z}_N$ duality web.

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