Confinement in Five Dimensions

TL;DR

This paper explores five-dimensional superconformal field theories using geometric limits of M-theory, revealing phases with confinement, massive vacua, and unbroken symmetries through the study of Ricci-flat metrics and instanton interactions.

Contribution

It introduces a geometric framework to analyze phases of 5d SCFTs, including confining vacua and coupled theories, by varying couplings and studying Ricci-flat metrics on Calabi-Yau singularities.

Findings

Many 5d SCFTs have confining vacua with unbroken 1-form symmetries.

Varying couplings leads to coupled SCFTs interacting via BPS instanton particles.

Complete Ricci flat metrics on quotient conifolds characterize the parameter space.

Abstract

Five dimensional super conformal field theories can be studied using their geometric realisation as a limit of $M$-theory on a metrically conical Calabi-Yau threefold. We utilise this framework to investigate the phases of such theories that arise by varying the couplings away from the conformal point. We demonstrate that many 5d SCFTs, including strongly coupled gauge theories, have couplings giving rise to massive, confining vacua with confining strings and corresponding unbroken 1-form symmetries. The simplest examples arise by considering the parameter space of {\it complete} Ricci flat metrics on discrete quotients of the standard conifold singularity. Varying other couplings produces coupled 5d SCFTs interacting via massive BPS instanton particle states.