Constant maps in equivariant topological strings and geometric modeling of fluxes

TL;DR

This paper develops an equivariant topological string framework on toric manifolds, incorporating constant maps to regularize non-compact Calabi-Yau spaces, and explores their implications for flux modeling and holography.

Contribution

It introduces a method to include constant maps in equivariant topological strings, linking flux compactifications with supergravity and proposing a non-perturbative holographic correspondence.

Findings

Regularization of non-compact Calabi-Yau spaces via constant maps

Explicit examples demonstrating finite genus expansion results

Proposal of a non-perturbative holographic match with M2-brane partition functions

Abstract

We study the equivariant generalization of topological strings on toric manifolds, focusing in particular on defining the contributions of constant maps in the genus expansion of the partition function. This approach regularizes the integration over non-compact Calabi-Yau spaces, producing finite results at each order in the expansion, as illustrated by a broad set of explicit examples. Our investigation highlights the geometric modeling of flux compactifications and clarifies the link between the effective supergravity framework and the equivariant topological string formalism, building on recent developments by Martelli and Zaffaroni. We conclude that the connection between topological string theory and supergravity/field theory involves switching between geometric moduli and fluxes, shedding light on the role of ensemble averages in string theory. We propose an exact non-perturbative holographic match with the corresponding M2-brane partition functions, which we test perturbatively at all orders in the gauge group rank $N$ in a companion paper. A special case of our proposal for vanishing flux reformulates the Ooguri-Strominger-Vafa conjecture within the equivariant topological string framework.