M-theory interpretation of the real topological string

TL;DR

This paper provides an M-theory interpretation of the unoriented topological string, connecting it to BPS M2-brane states and generalizing the BPS integer expansion, with implications for tadpole cancellation and previous literature.

Contribution

It introduces a novel M-theory lift of the unoriented topological string and clarifies its relation to BPS invariants and tadpole conditions, extending prior conjectures.

Findings

M-theory lift computes open and unoriented amplitudes via BPS M2-branes.

Integer multiplicities relate to equivariant Gopakumar-Vafa invariants.

Provides new insights into tadpole cancellation conditions.

Abstract

We describe the type IIA physical realization of the unoriented topological string introduced by Walcher, describe its M-theory lift, and show that it allows to compute the open and unoriented topological amplitude in terms of one-loop diagram of BPS M2-brane states. This confirms and allows to generalize the conjectured BPS integer expansion of the topological amplitude. The M-theory lift of the orientifold is freely acting on the M-theory circle, so that integer multiplicities are a weighted version of the (equivariant subsector of the) original closed oriented Gopakumar-Vafa invariants. The M-theory lift also provides new perspective on the topological tadpole cancellation conditions. We finally comment on the M-theory version of other unoriented topological strings, and clarify certain misidentifications in earlier discussions in the literature.