Star shaped quivers in four dimensions

TL;DR

This paper presents a 4d Lagrangian description of compactifications of 6d minimal conformal matter theories, using star-shaped quivers to encode various punctures and fluxes, enabling the construction of across-dimension duals.

Contribution

It introduces a star-shaped quiver gauge theory that captures the IR duals of 6d to 4d compactifications with arbitrary punctures and fluxes, providing a unified Lagrangian framework.

Findings

Lagrangian describes compactifications with arbitrary punctures and flux.

Star-shaped quiver encodes the data of 6d theories in 4d.

Enables construction of across-dimension duals for diverse compactifications.

Abstract

We discuss a 4d Lagrangian descriptions, across dimensions IR dual, of compactifications of the 6d $(\text{D},\text{D})$ minimal conformal matter theory on a sphere with arbitrary number of punctures and a particular value of flux as a gauge theory with a simple gauge group. The Lagrangian has the form of a ``star shaped quiver'' with the rank of the central node depending on the 6d theory and the number and type of punctures. Using this Lagrangian one can construct across dimensions duals for arbitrary compactifications (any, genus, any number and type of $\text{USp}$ punctures, and any flux) of the $(\text{D},\text{D})$ minimal conformal matter gauging only symmetries which are manifest in the UV.