Genus-One data and Anomaly Detection

TL;DR

This paper introduces genus-one data as a tool to detect anomalies in (1+1)-dimensional theories with finite group symmetries, highlighting its effectiveness and limitations depending on the group structure.

Contribution

It defines genus-one data for anomaly detection in (1+1)d theories and characterizes which finite groups it can effectively analyze.

Findings

Genus-one data detects anomalies for certain finite groups.

It is ineffective for dicyclic groups.

Provides criteria for the applicability of genus-one data.

Abstract

We introduce the notion of genus-one data for theories in (1+1)-dimensions with an anomalous finite group global symmetry. We outline the groups for which genus-one data is effective in detecting the anomaly, and also show that genus-one data is insufficient to detect the anomaly for dicyclic groups.