Vacuum Structures Revisited

TL;DR

This paper explores the structure of vacua in supersymmetric gauge theories across dimensions, revealing how higher symmetries and field configurations lead to vacuum decomposition into multiple universes, with implications for topological sectors.

Contribution

It introduces a framework including field strength in vacuum moduli and demonstrates vacuum decomposition in theories with $ ext{Z}_p$ symmetry, extending existing results across dimensions.

Findings

Vacua decompose into p universes at an intermediate scale.

Inclusion of field strength in vacuum moduli affects symmetry and decomposition.

Proposes a UV gauge theory with restricted instanton sectors for super Yang-Mills.

Abstract

We consider the relationship between the higher symmetry and the dynamical decomposition in supersymmetric gauge theory in various dimensions by studying the semi-classical potential energy. We observe that besides the scalar moduli we shall also include the field strength $F_{0\cdots d}$ in the vacuum moduli in the 1+d dimensional theory along with a $\mathbb{Z}_{p}$ $d$-form symmetry. In gauge theory for charge-$p$ matters with this symmetry, we find that the vacua decompose into $p$ different universes at an intermediate scale, which means no dynamical domain wall can interpolate between them. In our setup, we re-derive the existing results on the decomposition in various dimensions. In four dimensions, we propose a UV gauge theory for the generalized super Yang-Mills theory, whose instanton sectors are restricted to the topological number with integer multiples of $p$.