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(Non-)Abelian discrete anomalies

Takeshi Araki, Tatsuo Kobayashi, Jisuke Kubo, Saul Ramos-Sanchez, Michael Ratz, Patrick K. S. Vaudrevange

TL;DR

This work derives anomaly constraints for both Abelian and non-Abelian discrete symmetries using a path-integral (Fujikawa) approach and applies them to heterotic orbifold models, where discrete anomalies are shown to originate from the anomalous $U(1)$ and its geometric counterpart, the anomalous space-group element. The authors demonstrate universal Green-Schwarz cancellation of basic anomalies and reveal intricate relations among $k$-anomalies, flavor, $R$-symmetries, and $T$-duality anomalies, including connections to $T$-dependent threshold corrections. They also discuss how FI-term cancellation in supersymmetric vacua generically breaks anomalous $U(1)$ and often the associated discrete symmetries, with potential implications for the emergence of approximate flavor structures. Overall, the results provide a structured map from geometric/auxiliary string data to low-energy discrete anomalies and their consistent cancellation mechanisms, offering guidance for string-model building and phenomenology of approximate symmetries.

Abstract

We derive anomaly constraints for Abelian and non-Abelian discrete symmetries using the path integral approach. We survey anomalies of discrete symmetries in heterotic orbifolds and find a new relation between such anomalies and the so-called `anomalous' U(1).

(Non-)Abelian discrete anomalies

TL;DR

This work derives anomaly constraints for both Abelian and non-Abelian discrete symmetries using a path-integral (Fujikawa) approach and applies them to heterotic orbifold models, where discrete anomalies are shown to originate from the anomalous and its geometric counterpart, the anomalous space-group element. The authors demonstrate universal Green-Schwarz cancellation of basic anomalies and reveal intricate relations among -anomalies, flavor, -symmetries, and -duality anomalies, including connections to -dependent threshold corrections. They also discuss how FI-term cancellation in supersymmetric vacua generically breaks anomalous and often the associated discrete symmetries, with potential implications for the emergence of approximate flavor structures. Overall, the results provide a structured map from geometric/auxiliary string data to low-energy discrete anomalies and their consistent cancellation mechanisms, offering guidance for string-model building and phenomenology of approximate symmetries.

Abstract

We derive anomaly constraints for Abelian and non-Abelian discrete symmetries using the path integral approach. We survey anomalies of discrete symmetries in heterotic orbifolds and find a new relation between such anomalies and the so-called `anomalous' U(1).

Paper Structure

This paper contains 44 sections, 68 equations, 1 figure, 7 tables.

Table of Contents

  1. Introduction
  2. Anomaly-free discrete symmetries
  3. A few words on symmetries
  4. Basics of anomalies
  5. Anomaly constraints for continuous symmetries
  6. (Re-)Derivation of anomaly constraints for $\boldsymbol{\mathbbm{Z}_N}$ symmetries
  7. Anomalies of non-Abelian discrete symmetries
  8. Summary of anomaly constraints
  9. Consequences of discrete anomalies
  10. A comment on the 'SUSY zero mechanism'
  11. Anomalies in heterotic orbifold models
  12. Orbifold basics
  13. Stringy discrete symmetries
  14. Space group rules
  15. Discrete $\boldsymbol{R}$-symmetries
  16. ...and 29 more sections

Figures (1)

  • Figure 1: Triangle diagrams.