First Order String Theory and the Kodaira-Spencer Equations. I

TL;DR

This paper investigates first-order bosonic string theory with target-space complex structure deformations, showing that conformal invariance enforces the Kodaira-Spencer equations on Beltrami differentials, and explores the theory's symmetries and reformulations.

Contribution

It derives the effective action for first-order string theory with complex structure deformations and demonstrates the necessity of Kodaira-Spencer equations for conformal invariance.

Findings

Conformal invariance requires Kodaira-Spencer equations.

Effective action derived for deformed string theory.

Reformulation in terms of vielbein background fields.

Abstract

We consider first-order bosonic string theory, perturbed by the primary operator, corresponding to deformation of the target-space complex structure. We compute the effective action in this theory and find that its consistency with the world-sheet conformal invariance requires necessarily the Kodaira-Spencer equations to be satisfied by target-space Beltrami differentials. We discuss the symmetries of the theory and its reformulation in terms of the vielbein background fields.