Large N Field Theory of N=2 Strings and Self-Dual Gravity

TL;DR

This paper reviews the construction of self-dual gravity and ${ m N}=2$ string field theory using large $N$ two-dimensional sigma models, highlighting the algebraic structures and background formulations involved.

Contribution

It introduces a large $N$ Wess-Zumino-Witten model framework for ${ m N}=2$ strings and analyzes its canonical structure and current algebra.

Findings

Identification of an infinite-dimensional Poisson algebra of currents

Formulation of the theory via a large $N$ Wess-Zumino-Witten model

Analysis of the canonical structure in a nontrivial background

Abstract

We review some aspects of the construction of self-dual gravity and the associated field theory of ${\cal N}=2$ strings in terms of two-dimensional sigma models at large $N$. The theory is defined through a large $N$ Wess-Zumino-Witten model in a nontrivial background and in a particular double scaling limit. We examine the canonical structure of the theory and describe an infinite-dimensional Poisson algebra of currents.