Two Dimensional Kodaira-Spencer Theory and Three Dimensional Chern-Simons Gravity

TL;DR

This paper develops a two-dimensional Kodaira-Spencer theory linked to the topological B-model on Riemann surfaces, revealing symmetries and connections to three-dimensional gravity and topological M theory.

Contribution

It formulates a 2D Kodaira-Spencer theory for Calabi-Yau threefolds and connects it to recursion relations and SL(2,R) symmetry, supporting the existence of topological M theory.

Findings

Ward identities match Eynard-Orantin recursion relations

Reveals hidden affine SL(2,R) symmetry

Provides evidence for topological M theory

Abstract

Motivated by the six dimensional formulation of Kodaira-Spencer theory for Calabi-Yau threefolds, we formulate a two dimensional version and argue that this is the relevant field theory for the target space of local topological B-model with a geometry based on a Riemann surface. We show that the Ward identities of this quantum theory is equivalent to recursion relations recently proposed by Eynard and Orantin to solve the topological B model. Our derivation provides a conceptual explanation of this link and reveals a hidden affine SL(2,R) symmetry. Moreover we argue that our results provide the strongest evidence yet of the existence of topological M theory in one higher dimension, which in this case can be closely related to SL(2,R)Chern-Simons formulation of three dimensional gravity.