A Heterotic K\"ahler Gravity and the Distance Conjecture

TL;DR

This paper develops a new holomorphic field theory derived from heterotic string theory deformations, exploring its properties and connections to the swampland distance conjecture, and introduces a novel symplectic cohomology framework.

Contribution

It introduces a new holomorphic theory from heterotic superpotential deformations and defines a novel symplectic cohomology related to complex structure moduli.

Findings

Connections to the swampland distance conjecture are established.

A new symplectic cohomology theory is formulated.

The theory simplifies at large fluxes or distances in moduli space.

Abstract

Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the complex structure deformations (the Beltrami differential). Treated separately, for large fluxes, or alternatively at large distances in the background complex structure moduli space, these fields can be integrated out to obtain a new field theory in the remaining fields, which describe the complexified hermitian and gauge degrees of freedom. We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. In the process, we define a new type of symplectic cohomology theory, where the background complex structure Beltrami differential plays the role of the symplectic form.