M-Theory and Topological Strings--I

TL;DR

This paper reveals a simple M-theory interpretation for certain topological string amplitudes on Calabi-Yau 3-folds, connecting string contributions to M-theory computations involving wrapped M2 branes and Kaluza-Klein modes, and linking to large N Chern-Simons theory.

Contribution

It provides a novel M-theory perspective on topological string amplitudes, including contributions from instantons and a connection to large N Chern-Simons theory.

Findings

M-theory one-loop computations reproduce all genus string contributions.

Contributions from small worldsheet instantons are explicitly obtained.

Large N Chern-Simons theory can compute these gravitational terms in special cases.

Abstract

The $R^2 F^{2g-2}$ terms of Type IIA strings on Calabi-Yau 3-folds, which are given by the corresponding topological string amplitudes (a worldsheet instanton sum for all genera), are shown to have a simple M-theory interpretation. In particular, a Schwinger one-loop computation in M-theory with wrapped M2 branes and Kaluza-Klein modes going around the loop reproduces the all genus string contributions from constant maps and worldsheet instanton corrections. In the simplest case of an isolated M2 brane with the topology of the sphere, we obtain the contributions of small worldsheet instantons (sphere ``bubblings'') which extends the results known or conjectured for low genera. Surprisingly, the 't Hooft expansion of large $N$ Chern-Simons theory on $S^3$ can also be used in a novel way to compute these gravitational terms at least in special cases.