Confinement of 3d $\mathcal{N}=2$ Gauge Theories from M-theory on CY4

TL;DR

This paper introduces a new geometric transition in non-compact Calabi-Yau 4-folds that models confinement in 3d $ ext{N}=2$ $SU(N)$ gauge theories, with implications for understanding their global symmetries and phases.

Contribution

It presents a novel geometric smoothing of Calabi-Yau 4-fold singularities that corresponds to the confined phase of 3d $ ext{N}=2$ gauge theories, including the realization of confining strings as M2-branes.

Findings

Discovered a new smoothing of CY4 singularities via partial resolution and deformation.

Interpreted the smoothing as a confined phase for 3d $ ext{N}=2$ $SU(N)$ gauge theories.

Computed generalized global symmetries and SymTFT actions using topology and intersection theory.

Abstract

In this work, we present a new geometric transition in non-compact Calabi-Yau 4-folds, specifically for the cone over the 7d Sasaki-Einstein manifold $Q^{\scriptscriptstyle(1,1,1)}/\mathbb{Z}_{N}$. We discover a new smoothing of such Calabi-Yau 4-fold singularity via a partial resolution+deformation, which can be interpreted as a confined phase for a 3d $\mathcal{N}=2$ $SU(N)$ gauge theory. The confining strings are realized as M2-branes wrapping the torsional 1-cycles in this new geometric phase. We have also computed the generalized global symmetries, including finite $(-1)$-form symmetries, and SymTFT action using the link topology and intersection numbers of the resolved Calabi-Yau 4-fold.