Five-Dimensional Gauge Theories from Shifted Web Diagrams

TL;DR

This paper explores how shifted web diagrams extend the engineering of gauge theories from six to five dimensions, revealing new quiver gauge theories with specific matter content.

Contribution

It introduces the use of shifted toric web diagrams to engineer five-dimensional gauge theories from six-dimensional parent theories, expanding the geometric framework.

Findings

Shifted web diagrams can produce 5D quiver gauge theories.

Matter content is derived from 6D parent theories.

Examples illustrate the geometric-engineering correspondence.

Abstract

In previous works (arXiv:1610.07916, arXiv:1711.07921, arXiv:1807.00186) we studied a class of toric Calabi-Yau threefolds which engineer six-dimensional supersymmetric gauge theories with gauge group $U(N)$ and adjoint matter. The K\"ahler moduli space of these manifolds can be extended through flop transformations to include regions which are described by so-called shifted toric web diagrams. In this paper we analyse gauge theories that are engineered by these shifted toric web diagrams and argue that in specific limits, some of the them engineer five-dimensional quiver gauge theories with gauge group $G\subset U(N)$ and with fundamental and bi-fundamental matter. We discuss several examples in detail and describe how the matter sector is obtained from the six-dimensional parent theory.