Related papers: 3D Quantum Hyperbolic Field Theory

To understand what does Chern-Simons with compact Lie group(does not like Dijkgraaf-Witten model with finite group in 3d) attach to a point, we first give a construction of Topological Quantum Field Theory(TQFT) via Chern-Simons theory in…

We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory,…

A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.

We identify and study a class of hyperbolic 3-manifolds (which we call Macfarlane manifolds) whose quaternion algebras admit a geometric interpretation analogous to Hamilton's classical model for Euclidean rotations. We characterize these…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

We consider string/M-theory reductions on a compact space $X=X^\text{loc} \cup X^\circ$, where $X^\text{loc}$ contains the singular locus, and $X^\circ$ its complement. For the resulting supergravity theories, we construct a suitable…

Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review…

The goal of this work, motivated by the desire to understand causality in classical and quantum gravity, is an in depth investigation of causality in classical field theories with quasilinear equations of motion, of which General Relativity…

One of the general strategies for realizing a wide class of interacting QFTs is via junctions and intersections of higher-dimensional bulk theories. In the context of string/M-theory, this includes many $D > 4$ superconformal field theories…

We review the representation theory of the quantum group $U_\epsilon sl_2\mathbb{C}$ at a root of unity $\epsilon$ of odd order, focusing on geometric aspects related to the 3-dimensional quantum hyperbolic field theories (QHFT). Our…

Building on the work of Gang, Kang, and Kim arXiv:2405.16377, we propose 3D bulk dual field theories for 2D $\mathcal{N}=1$ supersymmetric minimal models $SM(P, Q)$ and $W_{N}$ algebra minimal models $W_{N}(P, Q)$. We associate to $SM(P,…

This paper is about algebro-geometrical structures on a moduli space $\CM$ of anomaly-free BV QFTs with finite number of inequivalent observables or in a finite superselection sector. We show that $\CM$ has the structure of F-manifold -- a…

This paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a smooth family of observable algebras. Using…

A 3-dimensional topological quantum field theory (TQFT) is a symmetric monoidal functor from the category of 3-cobordisms to the category of vector spaces. Such TQFTs provide in particular numerical invariants of closed 3-manifolds such as…

We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological…

Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the GFT fields depend on variables associated to vertices of the associated simplicial…

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT$_\pm [\mathcal{T}_{\rm rank \;0}]$, to a (2+1)D interacting $\mathcal{N}=4$ superconformal field theory (SCFT) $\mathcal{T}_{\rm…

We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field…

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…

Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…