Arjan Keurentjes — Page 2

arXiv1999

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

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.

hep-th↗

arXiv1999

Non-trivial flat connections on the 3-torus I: G_2 and the orthogonal groups

We propose a construction of non-trivial vacua for Yang-Mills theories on the 3-torus. Although we consider theories with periodic boundary conditions, twisted boundary conditions play an essential auxiliary role in our construction. In this article we will limit ourselves to the simplest case, based on twist in SU(2) subgroups. These reproduce the recently constructed new vacua for SO(N) and G_2 theories on the 3-torus. We show how to embed the results in the other exceptional groups F_4 and E_{6,7,8} and how to compute the relevant unbroken subgroups. In a subsequent article we will generalise to SU(N > 2) subgroups. The number of vacua found this way exactly matches the number predicted by the calculation of the Witten index in the infinite volume.

hep-th↗