Towards a gauge theory interpretation of the real topological string

TL;DR

This paper explores the real topological string on non-compact toric Calabi-Yau three-folds, using M-theory to compute invariants and proposing a gauge theory interpretation of orientifold effects and surface operators.

Contribution

It introduces a new gauge theoretical perspective on real topological strings and computes real Gopakumar-Vafa invariants via M-theory lift for various geometries.

Findings

Real topological string amplitudes exhibit sign changes across flop transitions.

Real BPS invariants remain continuous despite amplitude discontinuities.

Preliminary gauge theory description of orientifold effects and surface operators is proposed.

Abstract

We consider the real topological string on certain non-compact toric Calabi-Yau three-folds X, in its physical realization describing an orientifold of type IIA on X with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane BPS states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.