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

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.

19 pages

References in corpus (6)

• Quantum Background Independence In String Theory
• Holomorphic anomaly and matrix models
• Chiral Deformations of Conformal Field Theories
• On the partition sum of the NS five-brane
• Lectures on Wakimoto modules, opers and the center at the critical level
• Invariants of algebraic curves and topological expansion

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• Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
• The spectral curve of the Eynard-Orantin recursion via the Laplace transform
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• Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
• Aspects géométriques et intégrables des modèles de matrices aléatoires
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