M-theory and the string genus expansion

TL;DR

This paper explores how M-theory membranes relate to string theory, revealing that the dilaton coupling in string theory originates from quantum effects in membrane partition functions with specific topologies.

Contribution

It demonstrates that the dilaton coupling in string theory arises from quantum aspects of membrane partition functions in M-theory.

Findings

The membrane partition function with topology S^1 x Σ is analyzed.

The dilaton coupling to the string world sheet is shown to be quantum in origin.

A careful measure treatment reveals the M-theory origin of the dilaton coupling.

Abstract

The partition function of the membrane is investigated. In particular, the case relevant to perturbative string theory of a membrane with topology $S^1 \times \Sigma$ is examined. The coupling between the string world sheet Euler character and the dilaton is shown to arise from a careful treatment of the membrane partition function measure. This demonstrates that the M-theory origin of the dilaton coupling to the string world sheet is quantum in nature.