Large N WZW Field Theory Of N=2 Strings

TL;DR

This paper investigates the quantum aspects of a large N WZW sigma model for N=2 strings, revealing a generated (2,2) spacetime, vanishing higher-point functions at tree level, and a finite one-loop 3-point amplitude.

Contribution

It demonstrates that a large N WZW model reproduces key features of N=2 string field theory, including spacetime generation and finiteness of amplitudes.

Findings

A (2,2) spacetime is generated from the model.

Higher-point functions vanish at tree level.

One-loop 3-point amplitude is ultraviolet finite.

Abstract

We explore the quantum properties of self-dual gravity formulated as a large $N$ two-dimensional WZW sigma model. Using a non-trivial classical background, we show that a $(2,2)$ space-time is generated. The theory contains an infinite series of higher point vertices. At tree level we show that, in spite of the presence of higher than cubic vertices, the on-shell 4 and higher point functions vanish, indicating that this model is related with the field theory of closed N=2 strings. We examine the one-loop on-shell 3-point amplitude and show that it is ultra-violet finite.