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arXiv · 0711.1932

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

Robbert Dijkgraaf·Cumrun Vafa
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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.

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Robbert Dijkgraaf, Cumrun Vafa. 2007-11-13. Two Dimensional Kodaira-Spencer Theory and Three Dimensional Chern-Simons Gravity. https://arxiv.org/abs/0711.1932

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