Holography, 1-Form Symmetries, and Confinement

TL;DR

This paper explores the holographic description of confinement in 4d $ ext{SU}(N)$ Super-Yang Mills, focusing on 1-form symmetries, their anomalies, and their relation to chiral symmetry breaking, using supergravity duals and topological field theories.

Contribution

It identifies the topological couplings and anomalies related to 1-form symmetry in the holographic dual of 4d SYM and connects them to chiral symmetry breaking and IR topological field theories.

Findings

Identification of topological couplings determining 1-form symmetry

Matching of mixed anomalies with IR topological field theory

Derivation of anomalies from Little String Theory realization

Abstract

We study confinement in 4d $\mathcal{N}=1$ $SU(N)$ Super-Yang Mills (SYM) from a holographic point of view, focusing on the 1-form symmetry and its relation to chiral symmetry breaking. In the 5d supergravity dual, obtained by truncation of the Klebanov-Strassler solution, we identify the topological couplings that determine the 1-form symmetry and its 't Hooft anomalies. One such coupling is a mixed 0-form/1-form symmetry anomaly closely related to chiral symmetry breaking in gapped confining vacua. From the dual gravity description we also identify the infra-red (IR) 4d topological field theory (TQFT), which realises chiral symmetry breaking and matches the mixed anomaly. Finally, complementing this, we derive the chiral and mixed anomalies from the Little String Theory realization of pure SYM.