BCOV on the Large Hilbert Space

TL;DR

This paper reformulates BCOV theory of complex structure deformations using super moduli space, revealing connections to superstring field theory and employing large Hilbert space techniques for BV-extension.

Contribution

It introduces a novel formulation of BCOV theory as a pull-back to super moduli space, linking it to superstring field theory and large Hilbert space methods.

Findings

Manifest BV-extension in the new formulation

Resolution of non-local kinetic terms via auxiliary fields

Inclusion of a holomorphic 3-form compensator

Abstract

We formulate the BCOV theory of deformations of complex structures as a pull-back to the super moduli space of the worldline of a spinning particle. In this approach the appearance of a non-local kinetic term in the target space action has the same origin as the mismatch of pictures in the Ramond sector of super string field theory and is resolved by the same type of auxiliary fields in shifted pictures. The BV-extension is manifest in this description. A compensator for the holomorphic 3-form can be included by resorting to a description in the large Hilbert space.