# Introductory lectures on topological quantum field theory

@article{Carqueville2017IntroductoryLO, title={Introductory lectures on topological quantum field theory}, author={Nils Carqueville and Ingo Runkel}, journal={arXiv: Quantum Algebra}, year={2017} }

These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the definition in terms symmetric monoidal categories, and we highlight the algebraic formulation emerging from a formal generators-and-relations description. This allows one to understand (oriented, closed) 1- and 2-dimensional TQFTs in terms of a finite amount of…

## 18 Citations

### Introduction to 2-dimensional Topological Quantum Field Theory

- Mathematics
- 2022

Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of…

### Topological Quantum Field Theories for character varieties

- Mathematics
- 2018

This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful…

### Area-Dependent Quantum Field Theory

- Mathematics
- 2020

Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real…

### Reflection Positivity: A Quantum Field Theory Connection

- Mathematics, Physics
- 2019

At the heart of constructive quantum field theory lies reflection positivity. Through its use one may extend results for a Euclidean field theory to a relativistic theory. In this dissertation we…

### GRAU DE MATEMÀTIQUES Treball final de grau

- Mathematics
- 2020

Topological quantum field theories (TQFTs) are functors from the category of bordisms to the category of vector spaces that preserve their monoidal structure. Such functors arose in Physics but have…

### 2d TQFTs and baby universes

- PhysicsJournal of High Energy Physics
- 2021

Abstract
In this work, we extend the 2d topological gravity model of [1] to have as its bulk action any open/closed TQFT obeying Atiyah’s axioms. The holographic duals of these topological gravity…

### Equational theories of endomorphism monoids of categories with a topological flavor

- Mathematics
- 2020

It is shown that the endomorphism monoids of the category $2\mathfrak{Cob}$ of all $2$-cobordisms do not have finitely axiomatizable equational theories. The same holds for the {topological annular…

### Orbifolds of Reshetikhin-Turaev TQFTs

- Mathematics
- 2018

We construct three classes of generalised orbifolds of Reshetikhin-Turaev theory for a modular tensor category $\mathcal{C}$, using the language of defect TQFT from [arXiv:1705.06085]: (i) spherical…

### Phase Space on a Surface with Boundary via Symplectic Reduction

- Mathematics, Physics
- 2021

We describe the symplectic reduction construction for the physical phase space in gauge theory and apply it for the BF theory. Symplectic reduction theorem allows us to rewrite the same phase space…

### The Representation Theory of Brauer Categories I: Triangular Categories

- MathematicsApplied Categorical Structures
- 2022

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the…

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