Chiral Ring of Strange Metals: The Multicolor Limit

TL;DR

This paper investigates the chiral ring structure of a family of supersymmetric conformal field theories derived from dense 2D adjoint QCD in the large color limit, revealing a connection to Schur polynomials.

Contribution

It determines the chiral ring in the multicolor limit, showing it is generated by Schur polynomials, extending previous work for small N.

Findings

Chiral primaries are labeled by partitions.

The chiral ring is isomorphic to the ring of Schur polynomials.

Results constrain dual string theory descriptions.

Abstract

The low energy limit of a dense 2D adjoint QCD is described by a family of ${\cal N}=(2,2)$ supersymmetric coset conformal field theories. In previous work we constructed chiral primaries for a small number $N < 6$ of colors. Our aim in the present note is to determine the chiral ring in the multicolor limit where $N$ is sent to infinity. We shall find that chiral primaries are labeled by partitions and identify the ring they generate as the ring of Schur polynomials. Our findings impose strong constraints on the possible dual description through string theory in an $AdS_3$ compactification.