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

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 $Q^{(1,1,1)}/{\mathbb{Z}}_N$. 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.

46 pages V2: Added a new Section 4.2 introducing the proposed form of the CY4 metric for the deformed-resolved phase

Cited by in corpus (1)

• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories