The Covariant Chiral Ring

TL;DR

This paper constructs a covariant generating function for chiral primaries in symmetric orbifold CFTs with N=(4,4) supersymmetry, revealing representation content and linking to string dualities and Lorentz covariance.

Contribution

It introduces a covariant generating function for the chiral ring in symmetric orbifold CFTs, connecting representation theory with string dualities and Lorentz covariance.

Findings

Captures SO(21) and SO(5) representation content for K3 and T4 seed spaces.

Relates chiral ring transformation properties to string dualities.

Links moduli space isometries to Lorentz covariance of string partition functions.

Abstract

We construct a covariant generating function for the spectrum of chiral primaries of symmetric orbifold conformal field theories with N=(4,4) supersymmetry in two dimensions. For seed target spaces K3 and T4, the generating functions capture the SO(21) and SO(5) representation theoretic content of the chiral ring respectively. Via string dualities, we relate the transformation properties of the chiral ring under these isometries of the moduli space to the Lorentz covariance of perturbative string partition functions in flat space.