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We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1 \times M_3$ with a non-trivial holonomy of a discrete global symmetry along the $S^1$.…
We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The…
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the…
We propose a quantum field theory (QFT) method to approach the classification of indefinite sector of Kac-Moody algebras. In this approach, Vinberg relations are interpreted as the discrete version of the QFT_{2} equation of motion of a…
Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of…
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…
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…
Rovelli's relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute, but it is relative to the observer itself. The interpretation goes further and…
The concept of a "space of quantum field theories" or "theory space" was set out in the 1970's in work of Wilson, Friedan and others. This structure should play an important role in organizing and classifying QFTs, and in the study of the…
We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
We provide a detailed analysis of the classical and quantized theory of a multiplet of inhomogeneous Klein-Gordon fields, which couple to the spacetime metric and also to an external source term; thus the solutions form an affine space.…
Consider a d-dimensional quantum field theory (QFT) $\mathfrak{T}$, with a generalized symmetry $\mathcal{S}$, which may or may not be invertible. We study the action of $\mathcal{S}$ on generalized or $q$-charges, i.e. $q$-dimensional…
The problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group to the algebra of sections of a sheaf of…