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.
Highlights
Theories with extended supersymmetry have interesting massive spectra protected against decay by the BPS constraint
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
Summary
Theories with extended supersymmetry have interesting massive spectra protected against decay by the BPS constraint (see e.g. [1]). The graph with nodes consisting of elliptically fibered Calabi-Yau manifolds and links describing the process of specializing complex structure to a singularity, resolving it by blowing up, is referred to as a Higgsing tree. We conjecture that the topological string partition functions of nodes of the Higgsing tree specialize upon moving towards the root of the tree according to maps J(g ) → J(g) relating the ring of Jacobi forms of the associated Weyl groups.. One parent theory (which on infinite length Higgsing trees would depend on infinitely many parameters) should capture all geometries subsumed in a Higgsing tree This perspective could offer a path towards the proof of our conjecture; the point to be addressed is that the topological string partition function exhibits singularities on the subslices of moduli space corresponding to the singular geometries. Review of elliptically fibered Calabi-Yau manifolds, and reproduces some rank 1 Higgsing trees for the reader’s convenience
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
