Averaging over moduli in deformed WZW models

TL;DR

This paper studies the ensemble of deformed WZW models, computes their average partition function, and suggests a holographic dual involving Chern-Simons theory, with mathematical insights into affine Lie algebra characters.

Contribution

It introduces a novel ensemble average of WZW models, interprets it as a sum over 3-manifolds, and connects it to holography and affine Lie algebra characters.

Findings

Average partition function as sum over 3-manifolds

Identification of a holographic dual involving Chern-Simons theory

Mathematical result: a Siegel-Weil formula for affine Lie algebra characters

Abstract

WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have $N$ abelian conserved currents and central charge $c > N$. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as $U(1)^{2N}$ Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.