Weyl invariant Jacobi forms along Higgsing trees

TL;DR

This paper uses topological string methods to compute BPS counting functions for 5d gauge theories derived from 6d SCFTs, revealing how Weyl invariant Jacobi forms govern their Higgsing tree structures.

Contribution

It introduces a novel approach linking Higgsing trees of 5d theories to homomorphisms between rings of Weyl invariant Jacobi forms, advancing understanding of symmetry enhancements.

Findings

Partition functions along Higgsing trees are determined by Weyl invariant Jacobi form homomorphisms.

Symmetry enhancements in gauge theories are inherited by BPS spectra.

Connections between symmetry enhancements and 1-form symmetries are identified.

Abstract

Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field theories upon circle compactification. Such theories are naturally organized in terms of nodes of Higgsing trees. We demonstrate that the specialization of the partition function as we move from the crown to the root of a tree is determined by homomorphisms between rings of Weyl invariant Jacobi forms. Our computations are made feasible by the fact that symmetry enhancements of the gauge theory which are manifest on the massless spectrum are inherited by the entire tower of BPS particles. In some cases, these symmetry enhancements have a nice relation to the 1-form symmetry of the associated gauge theory.