Formal solution of the master equation via HPT and deformation theory

Details Formal solution of the master equation via HPT and deformation theory Formal solution of the master equation via HPT and deformation theory

1999-06-06

arxiv.org/abs/math/9906036v2

Forum Mathematicum 14 (2002), 847-868

Mathematics

Algebraic Geometry

AMSTeX 2.1, 21 pages

Scientific paper

We construct a solution of the master equation by means of standard tools from homological perturbation theory under just the hypothesis that the ground field be of characteristic zero, thereby avoiding the formality assumption of the relevant Lie algebra. To this end we endow the homology H(g) of any differential graded Lie algebra g with an sh-Lie structure such that g and H(g) are sh-equivalent. We discuss our solution of the master equation in the context of deformation theory. Given the extra structure appropriate to the extended moduli space of complex structures on a Calabi-Yau manifold, the known solutions result as a special case.

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