Related papers: Algebraic orbifold conformal field theories

We give a general construction of correlation functions in rational conformal field theory on a possibly non-orientable surface with boundary in terms of 3-dimensional topological quantum field theory. The construction applies to any…

In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…

By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…

We discuss geometric aspects of orbifold conformal field theories in the moduli space of N=(4,4) superconformal field theories with central charge c=6. Part of this note consists of a summary of our earlier results on the location of these…

Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

We generalize the operadic approach to algebraic quantum field theory [arXiv:1709.08657] to a broader class of field theories whose observables on a spacetime are algebras over any single-colored operad. A novel feature of our framework is…

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…

We use the method of Bruinier--Raum to show that symmetric formal Fourier--Jacobi series, in the cases of norm-Euclidean imaginary quadratic fields, are Hermitian modular forms. Consequently, combining a theorem of Yifeng Liu, we deduce…

We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that are not distinguishable by observables. We…

This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…

We present an explicit basis for orders of arbitrary level N>1 in definite rational quaternion algebras. These orders have applications to computations of spaces of elliptic and quaternionic modular forms.

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

To a given algebraic curve we assign an infinite family of quantum curves (Schr\"odinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model…

Starting from an abelian rigid braided monoidal category C we define an abelian rigid monoidal category C_F which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational…

This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability.…

The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…

Picard groups of tensor categories play an important role in rational conformal field theory. The Picard group of the representation category C of a rational vertex algebra can be used to construct examples of (symmetric special) Frobenius…

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…

In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…