Chiral Algebras for Trinion Theories

TL;DR

This paper conjectures the complete set of generators for the chiral algebras associated with T_n theories in 4D N=2 superconformal theories, supported by explicit construction for T_4 and analysis of their structure.

Contribution

It proposes the full generator set for T_n chiral algebras and constructs the T_4 case, revealing new Higgs branch relations.

Findings

Conjectured the complete generator set for T_n chiral algebras.

Explicitly constructed the T_4 chiral algebra.

Discovered new Higgs branch chiral ring relations.

Abstract

It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T_n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T_n theories. We also explicitly construct the chiral algebra arising from the T_4 theory. Its null relations give rise to new T_4 Higgs branch chiral ring relations.