Non-trivial flat connections on the 3-torus II: The exceptional groups F_4 and E_6,7,8

TL;DR

This paper extends the construction of non-trivial gauge theory vacua on the 3-torus to exceptional groups F4 and E6,7,8, demonstrating their role in resolving the Witten index problem.

Contribution

It introduces new vacua for exceptional gauge groups on the 3-torus and calculates their unbroken subgroups and contributions to the Witten index.

Findings

Extra vacua for F4 and E6,7,8 groups identified

Unbroken subgroups and their contributions computed

Witten index problem resolved for these groups

Abstract

We continue the construction of non-trivial vacua for gauge theories on the 3-torus, started in hep-th/9901154. Application of constructions based on twist in SU(N) with N > 2 produce more extra vacua in theories with exceptional groups. We calculate the relevant unbroken subgroups, and their contribution to the Witten index. We show that the extra vacua we find in the exceptional groups are sufficient to solve the Witten index problem for these groups.