Large N WZW field theory of N=2 strings

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.

A New Approach to Superstring Field Theory

“…It is easy to show that the covariantized light-cone gluing prescription implies that [A, [B, C]]+[B, [C, A]]+[C, [A, B]] = 0, so the interaction term can be interpreted as the large N limit of an open string interaction term where [, ] for open strings is the usual commutator coming from the U(N) Chan-Paton factors. This is not so surprising since self-dual gravity can be interpreted as the large N limit of self-dual Yang-Mills, suggesting that the closed self-dual string can be interpreted as the large N limit of the open self-dual string [21]. If such an interpretation also holds for the N=2 superconformal field theory representing the ten-dimensional superstring, it might shed light on the duality relating N=4 super-Yang-Mills with the Type IIB superstring [22].…”

Topological gravity as large N topological gauge theory

“…In particular, self-dual gravity on T * S 2 can be viewed heuristically as the large N limit of the principal chiral series on S 2 . There have also been some checks of this equivalence at the quantum level [19] . This structure parallels that of the N = 2 topological string where the role of volume preserving diffeomorphisms is now played by SU (∞) which is the local group of area preserving diffeomorphisms .…”

$\mathcal{N} = 2$ STRING GEOMETRY AND THE HEAVENLY EQUATIONS

“…A different description of N = 2 strings in terms of a large N limit of a WZW field theory was proposed in Ref. [10]. The connection between N = 2 self-dual supergravity and N = 2 super-WZW was worked out in Ref.…”