The Real Topological Vertex at Work

TL;DR

This paper introduces a formalism for computing topological string partition functions with D-branes and O-planes on toric Calabi-Yau manifolds, connecting it to Chern-Simons theory and crystal melting models.

Contribution

It develops the real vertex formalism for orientifolded Calabi-Yau manifolds, including non-trivial fixed legs, and relates it to dualities and statistical models.

Findings

No perturbative contributions beyond one-loop.

Presence of non-perturbative sectors in the partition function.

Connection between real vertex and symmetric crystal melting model.

Abstract

We develop the real vertex formalism for the computation of the topological string partition function with D-branes and O-planes at the fixed point locus of an anti-holomorphic involution acting non-trivially on the toric diagram of any local toric Calabi-Yau manifold. Our results cover in particular the real vertex with non-trivial fixed leg. We give a careful derivation of the relevant ingredients using duality with Chern-Simons theory on orbifolds. We show that the real vertex can also be interpreted in terms of a statistical model of symmetric crystal melting. Using this latter connection, we also assess the constant map contribution in Calabi-Yau orientifold models. We find that there are no perturbative contributions beyond one-loop, but a non-trivial sum over non-perturbative sectors, which we compare with the non-perturbative contribution to the closed string expansion.