Higher-Form Symmetries in 5d

TL;DR

This paper investigates higher-form symmetries in 5d quantum field theories, establishing geometric criteria from Calabi-Yau intersection data, and explores their invariance under dualities and extensions to other M-theory compactifications.

Contribution

It introduces a geometric criterion for higher-form symmetries in 5d theories based on Calabi-Yau intersection data and tests it across various examples, including toric geometries.

Findings

Higher-form symmetries are characterized by intersection data in Calabi-Yau threefolds.

The geometric criterion is consistent with dualities and flop transitions.

Extensions to 4d theories from G2-holonomy manifolds are discussed.

Abstract

We study higher-form symmetries in 5d quantum field theories, whose charged operators include extended operators such as Wilson line and 't Hooft operators. We outline criteria for the existence of higher-form symmetries both from a field theory point of view as well as from the geometric realization in M-theory on non-compact Calabi-Yau threefolds. A geometric criterion for determining the higher-form symmetry from the intersection data of the Calabi-Yau is provided, and we test it in a multitude of examples, including toric geometries. We further check that the higher-form symmetry is consistent with dualities and is invariant under flop transitions, which relate theories with the same UV-fixed point. We explore extensions to higher-form symmetries in other compactifications of M-theory, such as $G_2$-holonomy manifolds, which give rise to 4d $\mathcal{N}=1$ theories.