Beta-gamma systems and the deformations of the BRST operator

Details Beta-gamma systems and the deformations of the BRST operator Beta-gamma systems and the deformations of the BRST operator

2009-04-15

arxiv.org/abs/0904.2234v2

J.Phys.A42:355401,2009

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 15 pages; minor revision, typos corrected, Journal of Physics A, in press

Scientific paper

10.1088/1751-8113/42/35/355401

We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their "infinite metric" limits, corresponding to the beta-gamma systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasiclassical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate, that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss possible algebraic approach to the study of beta-functions in sigma-models.

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