Form field theory on Calabi-Yau threefold

TL;DR

This paper explores dualities between form theories on Calabi-Yau threefolds, connecting them to string field theories and analyzing their independence from complex structures.

Contribution

It demonstrates Abelian duality between 2 and 3-form theories on CY3 and relates these to A model string field theory, including anomaly equations.

Findings

Establishes S-duality between 2 and 3-form theories on CY3.

Links 2-form theory to A model string field theory.

Derives holomorphic anomaly equations for CY3.

Abstract

We show how the natural Abelian duality of 2 and 3-form gravity theories on seven dimensional manifold CY3xS1, leads to an S-duality between 2 and 3-form theories on simply connected CY3. The massless sector of the 2-form field theory on CY3 corresponds to the A model string field theory. We discuss the complex structure independence of the 2-form theory for a general Kahler manifold and derive the holomorphic anomaly equations for simply connected CY3.