Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Line Defect Quantum Numbers & Anomalies

T. Daniel Brennan, Clay Cordova, Thomas T. Dumitrescu

TL;DR

The paper establishes a systematic link between symmetry fractionalization of line defects and 't Hooft anomalies in 4D gauge theories. By analyzing Maxwell theory as an IR fixed point reachable from various SU(2) theories via adjoint Higgsing and Yukawa couplings, it derives how line defects acquire projective G^(0) quantum numbers and how these fractionalizations encode discrete and mixed anomalies. The work computes explicit anomaly inflow expressions for multiple representations (fundamentals and adjoints) and shows consistency with perturbative chiral anomalies upon appropriate symmetry reductions. This framework provides a practical method to infer UV anomaly structures from IR line data and RG flows, with concrete results for SU(2) QCD-like theories and Adjoint QCD including gravitational and 1-form/0-form mixed anomalies.

Abstract

We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This phenomenon is known as symmetry fractionalization, and in general it signals the presence of certain discrete 't Hooft anomalies. We describe this in detail in the context of free Maxwell theory in four dimensions. This understanding allows us to deduce the 't Hooft anomalies of non-Abelian gauge theories with renormalization group flows into Maxwell theory by analyzing the fractional quantum numbers of dynamical magnetic monopoles. We illustrate this method in $SU(2)$ gauge theories with matter fermions in diverse representations of the gauge group. For adjoint matter, we uncover a mixed anomaly involving the 0-form and 1-form symmetries, extending previous results. For $SU(2)$ QCD with fundamental fermions, the 't Hooft anomaly for the 0-form symmetries that is encoded by the fractionalization patterns of lines in the Maxwell phase is a consequence of the familiar perturbative (triangle) anomaly.

Line Defect Quantum Numbers & Anomalies

TL;DR

The paper establishes a systematic link between symmetry fractionalization of line defects and 't Hooft anomalies in 4D gauge theories. By analyzing Maxwell theory as an IR fixed point reachable from various SU(2) theories via adjoint Higgsing and Yukawa couplings, it derives how line defects acquire projective G^(0) quantum numbers and how these fractionalizations encode discrete and mixed anomalies. The work computes explicit anomaly inflow expressions for multiple representations (fundamentals and adjoints) and shows consistency with perturbative chiral anomalies upon appropriate symmetry reductions. This framework provides a practical method to infer UV anomaly structures from IR line data and RG flows, with concrete results for SU(2) QCD-like theories and Adjoint QCD including gravitational and 1-form/0-form mixed anomalies.

Abstract

We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This phenomenon is known as symmetry fractionalization, and in general it signals the presence of certain discrete 't Hooft anomalies. We describe this in detail in the context of free Maxwell theory in four dimensions. This understanding allows us to deduce the 't Hooft anomalies of non-Abelian gauge theories with renormalization group flows into Maxwell theory by analyzing the fractional quantum numbers of dynamical magnetic monopoles. We illustrate this method in gauge theories with matter fermions in diverse representations of the gauge group. For adjoint matter, we uncover a mixed anomaly involving the 0-form and 1-form symmetries, extending previous results. For QCD with fundamental fermions, the 't Hooft anomaly for the 0-form symmetries that is encoded by the fractionalization patterns of lines in the Maxwell phase is a consequence of the familiar perturbative (triangle) anomaly.
Paper Structure (23 sections, 96 equations)

This paper contains 23 sections, 96 equations.

Table of Contents

  1. Introduction
  2. Line Defects and Anomalies in Maxwell Theory
  3. 1-Form Symmetries and Wilson-'t Hooft Lines
  4. 1-Form Symmetry Background Fields and Anomalies
  5. Restriction to Discrete 1-Form Symmetry
  6. Enriching by 0-Form Global Symmetry
  7. 0-Form Symmetry Fractionalization
  8. 0-Form Symmetry Background Fields and Anomalies
  9. Bosonic and Fermionic Lines
  10. Background Fields and $\text{Spin}_{c}$ Connections
  11. Gravitational Anomalies and All Fermion Electrodynamics
  12. Anomalies from RG Flows to Maxwell Theory
  13. Yukawa Couplings, Symmetries, and Bundles
  14. 0-Form Symmetries
  15. 1-Form Symmetry
  16. ...and 8 more sections