D>2 Topological String

TL;DR

This paper introduces a new class of topological string theories for dimensions greater than two, coupling 2D topological gravity with twisted N=2 superconformal matter, and explores their algebraic structure and solvability.

Contribution

It constructs a novel $D>2$ topological string model using twisted N=2 superconformal matter and analyzes its algebraic constraints and solvability at all genera.

Findings

Recursion relations for correlation functions derived.

Model satisfies Virasoro and $ ext{W}^{(k-2)}_{ ext{infinity}}$ constraints.

Model is completely solvable at arbitrary genus.

Abstract

A $D>2$ topological string is presented by coupling the $2d$ topological gravity with the twisted version of the $N=2$ superconformal matter with $c=3k/(k-2)$. The latter is shown to admit $k+1$ chiral primary fields from the $SL(2,R)_{k}/U(1)$ unitary irreducible representations. The analysis of topological contact interactions along with the consistency requirement lead to recursion relations of correlation functions, that are convertable to the Virasoro constraints on the perturbed partition function. It is further expected to satisfy the nonlinear $\hat{W}^{(k-2)}_{\infty}$ constraints associated with the graded algebra $SL(k,2)$, and thus the model is completely solvable at arbitrary genus of the surface.