Domain walls in super Yang-Mills: worldvolume TQFTs and deconfinement from semiclassics on $\mathbb{R}^3\times\mathbb{S}^1$

TL;DR

This paper investigates domain walls in supersymmetric Yang-Mills theory on , explicitly characterizing their electric fluxes, representations, and associated worldvolume TQFTs, and examines quark deconfinement on these walls across various gauge groups.

Contribution

It provides explicit semiclassical computations of domain wall properties, tests proposed worldvolume TQFTs, and introduces a new TQFT for E6 domain walls, advancing understanding of confinement and deconfinement mechanisms.

Findings

Complete agreement between semiclassical and TQFT character computations.

Proposed a new TQFT for E6 domain walls and validated it.

Demonstrated quarks can end on domain walls for all gauge groups.

Abstract

This work studies domain walls between chirally-separated vacua in supersymmetric Yang-Mills theory (SYM) on $\mathbb{R}^3\times\mathbb{S}^1$ in the semiclassical limit. For all gauge groups we explicitly find the electric fluxes of all BPS domain walls and fully characterize the representation that they form under the global symmetry of SYM. We compute the characters of these representations formed by the semiclassical domain walls. We also compute these characters for the worldvolume TQFTs appearing in the literature for $SU(N)$ and $Sp(N)$ gauge groups. We find complete agreement between the two computations, providing thus a dynamical test of the proposed worldvolume TQFTs. We also propose a new worldvolume TQFT for $E_6$ domain walls, subjecting it to the same tests. Finally, we study deconfinement of quarks on domain walls for all gauge groups. We show that for all gauge groups confining strings (stable in the abelianized regime) can end on domain walls, regardless of whether or not the group has a center.