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Let $p\geq5$ be a prime, we show that a non-pointed modular fusion category $\mathcal{C}$ is Grothendieck equivalent to $\mathcal{C}(\mathfrak{sl}_2,2(p-1))_A^0$ if and only if $\dim(\mathcal{C})=p\cdot u$, where $u$ is a certain totally…

Quantum Algebra · Mathematics 2022-09-12 Zhiqiang Yu

We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum…

Quantum Algebra · Mathematics 2009-11-13 Deepak Naidu , Dmitri Nikshych

We prove that any fusion category over $\mathbb{C}$ with exactly one non-invertible simple object is spherical. Furthermore, we classify all such categories that come equipped with a braiding.

Quantum Algebra · Mathematics 2011-02-24 Josiah Thornton

Gravitational anomalies can be realized on the boundary of topologically ordered states in one higher dimension and are described by topological orders in one higher dimension. In this paper, we try to develop a general theory for both…

Strongly Correlated Electrons · Physics 2014-05-23 Liang Kong , Xiao-Gang Wen

We construct two-dimensional N=(2,2) supersymmetric gauge theories with orthogonal and symplectic groups using branes and orientifold planes in Type IIA string theory. A number of puzzles regarding the construction, including the effect of…

High Energy Physics - Theory · Physics 2018-08-29 Oren Bergman , Eran Avraham

We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified polar decomposition theorem for monoidal equivalences between…

Quantum Algebra · Mathematics 2023-01-13 David Reutter

Despite recent advances in the lattice representation theory of (generalized) symmetries, many simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras. We…

Quantum Physics · Physics 2025-09-05 Yuhan Liu , Andras Molnar , Xiao-Qi Sun , Frank Verstraete , Kohtaro Kato , Laurens Lootens

We define fully exact module categories, a subclass of exact module categories over a finite braided tensor category that is stable under the relative Deligne product. In contrast, we demonstrate with examples in both zero and non-zero…

Quantum Algebra · Mathematics 2026-01-30 Azat M. Gainutdinov , Robert Laugwitz

In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…

Category Theory · Mathematics 2023-11-22 Sebastian Heinrich

We point out that for N=4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality groups of these theories are the Hecke groups with…

High Energy Physics - Theory · Physics 2009-11-11 Philip C. Argyres , Anton Kapustin , Nathan Seiberg

We show that a weakly integral braided fusion category C such that every simple object of C has Frobenius-Perron dimension at most 2 is solvable. In addition, we prove that such a fusion category is group-theoretical in the extreme case…

Quantum Algebra · Mathematics 2012-05-14 Sonia Natale , Julia Yael Plavnik

Four-dimensional N=1 supersymmetric Spin(N) gauge theories with matter in the vector and spinor representations are considered. Dual descriptions are known for some of these theories. It is noted that when masses are given to all fields in…

High Energy Physics - Theory · Physics 2010-02-03 Matthew J. Strassler

A Lie 2-algebra is a "categorified" version of a Lie algebra: that is, a category equipped with structures analogous those of a Lie algebra, for which the usual laws hold up to isomorphism. In the classical mechanics of point particles, the…

Mathematical Physics · Physics 2009-12-08 John C. Baez , Alexander E. Hoffnung , Christopher L. Rogers

An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of…

q-alg · Mathematics 2008-02-03 John C. Baez

Symmetric product orbifold theories are valuable due to their universal features at large $N$. Here we will demonstrate that they have features that are not as pervasive: we provide evidence of strange behaviour under deformations within…

High Energy Physics - Theory · Physics 2023-01-09 Nathan Benjamin , Suzanne Bintanja , Alejandra Castro , Jildou Hollander

Dyonic gaugings of four-dimensional supergravity typically exhibit a richer vacuum structure compared to their purely electric counterparts, but their higher-dimensional origin often remains more mysterious. We consider a class of dyonic…

High Energy Physics - Theory · Physics 2017-04-05 Gianluca Inverso , Henning Samtleben , Mario Trigiante

We classify all fusion categories for a given set of fusion rules with three simple object types. If a conjecture of Ostrik is true, our classification completes the classification of fusion categories with three simple object types. To…

Geometric Topology · Mathematics 2007-09-24 Tobias J. Hagge , Seung-Moon Hong

In this paper we study the relative tensor product of module categories over braided fusion categories using, in part, the notion of the relative center of a module category. In particular we investigate the canonical tensor category…

Quantum Algebra · Mathematics 2011-10-18 Justin Greenough

We show that the non-trivially associated tensor category constructed from left coset representatives of a subgroup of a finite group is a modular category. Also we give a definition of the character of an object in a ribbon category which…

Quantum Algebra · Mathematics 2007-05-23 M. M. Al-Shomrani , E. J. Beggs

We establish a correspondence between modules and spans of algebras within a general monoidal 2-category $\mathfrak{C}$. Specifically, for an algebra $A$ in $\mathfrak{C}$, we construct a normalized lax 3-functor from the 2-category of…

Category Theory · Mathematics 2025-12-03 Hao Xu