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Fusion 3-Categories for Duality Defects.

Lakshya Bhardwaj1, Thibault Décoppet2, Sakura Schäfer-Nameki1

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This summary is machine-generated.

This study introduces generalized Tambara-Yamagami fusion 3-categories (3TY) for quantum theories with self-duality defects. We explore their construction and graded extensions, revealing connections to topological field theories and defect classifications.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Category Theory
  • Mathematical Physics

Background:

  • Investigates fusion 3-categorical symmetries in (3+1)-dimensional quantum theories.
  • Focuses on self-duality defects realized via half-space gauging in theories with one-form symmetries.
  • Draws parallels to Tambara-Yamagami fusion 1-categories.

Purpose of the Study:

  • To construct and study graded extensions of the fusion 3-category 3Vect(A[1]).
  • To explore the structure of generalized Tambara-Yamagami fusion 3-categories (3TY).
  • To understand the role of duality defects and their relation to topological field theories.

Main Methods:

  • Utilizes Brauer-Picard and Picard 4-groupoids for category construction.
  • Employs a 3-categorical extension theory inspired by Etingof, Nikshych, and Ostrik.
  • Analyzes invertible bimodule 3-categories and the Drinfeld center of 3Vect(A[1]).

Main Results:

  • Establishes a framework for generalized Tambara-Yamagami fusion 3-categories (3TY).
  • Identifies the Witt group of braided fusion 1-categories within the 4-groupoids.
  • Characterizes topological defects via a sylleptic strongly fusion 2-category and classifies them using finite abelian groups with alternating 2-forms.
  • Relates Picard 4-groupoids to generalized Witt groups via twisted Deligne tensor products.

Conclusions:

  • Provides explicit computations for Z/2 and Z/4 graded 3TY categories.
  • Demonstrates the utility of categorical constructions for understanding defects in quantum theories.
  • Highlights the deep connections between symmetry, defects, and higher category theory.