The Partition Function in the Four-Dimensional Schwarz-type Topological Half-Flat Two-Form Gravity

TL;DR

This paper computes the partition functions of a four-dimensional topological gravity model on K3 and T^4 surfaces, revealing connections to moduli spaces of Einstein-Kähler forms and $ar ext{partial}$-torsions.

Contribution

It derives explicit partition functions for a novel topological gravity model, including one-loop corrections, on specific four-dimensional manifolds.

Findings

Partition functions expressed via $ar ext{partial}$-torsions.

Moduli spaces correspond to Einstein-Kähler form classes.

Results applicable to K3 and T^4 geometries.

Abstract

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat 2-form gravity model on K3-surface or T^4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein-K\"ahler forms (the hyperk\"ahler forms). The integrand of the partition function is represented by the product of some $\bar \partial$-torsions.