N=4 Topological Strings

TL;DR

This paper develops a topological string theory from an N=4 superconformal framework, unifying various string types and enabling new calculations of string amplitudes and superpotentials.

Contribution

It introduces a novel topological string theory based on N=4 superconformal symmetry, connecting superstrings and N=2 strings, and offers new methods for amplitude calculations.

Findings

Proves vanishing of all scattering amplitudes except three-point and partition function for self-dual N=2 string.

Shows topological partition function on K3 computes superpotential in harmonic superspace.

Provides a new amplitude calculation prescription free of total-derivative ambiguities.

Abstract

We show how to make a topological string theory starting from an $N=4$ superconformal theory. The critical dimension for this theory is $\hat c= 2$ ($c=6$). It is shown that superstrings (in both the RNS and GS formulations) and critical $N=2$ strings are special cases of this topological theory. Applications for this new topological theory include: 1) Proving the vanishing to all orders of all scattering amplitudes for the self-dual $N=2$ string with flat background, with the exception of the three-point function and the closed-string partition function; 2) Showing that the topological partition function of the $N=2$ string on the $K3$ background may be interpreted as computing the superpotential in harmonic superspace generated upon compactification of type II superstrings from 10 to 6 dimensions; and 3) Providing a new prescription for calculating superstring amplitudes which appears to be free of total-derivative ambiguities.