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Introduction to topological symmetry in QFT

Daniel S. Freed

Abstract

This brief note publicizes the quantum framework for symmetry that is developed in our joint paper arXiv:2209.07471 with Greg Moore and Constantin Teleman. We include additional motivation and an application to a selection rule for line defects in 4-dimensional gauge theories.

Introduction to topological symmetry in QFT

Abstract

This brief note publicizes the quantum framework for symmetry that is developed in our joint paper arXiv:2209.07471 with Greg Moore and Constantin Teleman. We include additional motivation and an application to a selection rule for line defects in 4-dimensional gauge theories.
Paper Structure (20 sections, 34 equations, 7 figures)

This paper contains 20 sections, 34 equations, 7 figures.

Table of Contents

  1. Motivation: Computations in representations of $\mathfrak{s}\mathfrak{l}_2{\mathbb R}$
  2. Motivation: Algebras
  3. Quiches and their action on quantum field theories
  4. Quotients
  5. Line defects in 4-dimensional theories with $BA$-symmetry

Figures (7)

  • Figure 1: A domain wall, a right boundary theory, and a left boundary theory
  • Figure 2: The interval used in the dimensional reduction \ref{['eq:12']}
  • Figure 3: $(\sigma ,\rho )$-module data on a field theory $F$
  • Figure 4: On the left, the structure isomorphism of the $(\sigma ,\rho )$-module structure on $F$; on the right, the definition of the quotient theory $F\!\!\!\bigm/\!\!\sigma$
  • Figure 5: The $q$-twisted quotient of $F$ by $BA'$
  • ...and 2 more figures

Theorems & Definitions (7)

  • Definition 1
  • Remark 1
  • Definition 2
  • Example 1: center symmetry in gauge theory
  • Definition 3
  • Example 2
  • Remark 2