6d/5d exceptional gauge theories from web diagrams

TL;DR

This paper constructs new web diagrams for 6d and 5d gauge theories derived from Higgsings of 6d conformal matter theories, enabling computation of their Nekrasov partition functions.

Contribution

It introduces novel web diagrams with trivalent and quadrivalent gluings for various 6d/5d theories, expanding the toolkit for analyzing these theories.

Findings

Constructed web diagrams for multiple 6d/5d theories.

Computed Nekrasov partition functions using topological vertex.

Connected Higgsings to circle and twisted compactifications.

Abstract

We construct novel web diagrams with a trivalent or quadrivalent gluing for various 6d/5d theories from certain Higgsings of 6d conformal matter theories on a circle. The theories realized on the web diagrams include 5d Kaluza-Klein theories from circle compactifications of the 6d $G_2$ gauge theory with 4 flavors, the 6d $F_4$ gauge theory with 3 flavors, the 6d $E_6$ gauge theory with 4 flavors and the 6d $E_7$ gauge theory with 3 flavors. The Higgsings also give rise to 5d Kaluza-Klein theories from twisted compactifications of 6d theories including the 5d pure SU(3) gauge theory with the Chern-Simons level 9 and the 5d pure SU(4) gauge theory with the Chern-Simons level 8. We also compute the Nekrasov partition functions of the theories by applying the topological vertex formalism to the newly obtained web diagrams.