Holomorphic supergravity in ten dimensions and anomaly cancellation

TL;DR

This paper develops a ten-dimensional holomorphic supergravity theory on Calabi-Yau five-folds, demonstrating anomaly cancellation and relating it to known supergravity and string theories through complex geometric and quantum field theoretic methods.

Contribution

It formulates a novel ten-dimensional holomorphic supergravity model that reproduces heterotic moduli equations and connects to existing theories via non-local field redefinitions.

Findings

One-loop partition function simplifies to holomorphic Ray-Singer torsions.

Anomaly factorizes similarly to $SO(32)$ and $E_8\times E_8$ supergravity.

Counter-terms reconstruct a double-extension complex related to heterotic moduli.

Abstract

We formulate a ten-dimensional version of Kodaira-Spencer gravity on a Calabi-Yau five-fold that reproduces the classical Maurer-Cartan equation governing supersymmetric heterotic moduli. Quantising this theory's quadratic fluctuations, we show that its one-loop partition function simplifies to products of holomorphic Ray-Singer torsions and exhibits an anomaly that factorises as in $SO(32)$ and $E_8\times E_8$ supergravity. Based on this, we conjecture that this theory is the $SU(5)$-twisted version of ten-dimensional $N=1$ supergravity coupled to Yang-Mills and show that is related to the type I Kodaira-Spencer theory of Costello-Li via a non-local field redefinition. The counter-terms needed to cancel the anomaly and retain gauge invariance for the one-loop effective theory reconstruct the differential of a recently discovered double-extension complex. This complex has non-tensorial extension classes and its first cohomology counts the infinitesimal moduli of heterotic compactifications modulo order $\alpha'^2$ corrections.