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

Understand

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.