Beta-gamma systems and the deformations of the BRST operator

Abstract

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.

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

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Cited by in corpus (8)

• Conformal Field Theory and Algebraic Structure of Gauge Theory
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Quasiclassical Lian-Zuckerman Homotopy Algebras, Courant Algebroids and Gauge Theory
• Homotopy Algebras of Differential (Super)forms in Three and Four Dimensions
• Peculiarities of beta functions in sigma models
• The Algebra of Diffeomorphisms from the World Sheet
• On higher order Leibniz identities in TCFT
• Sigma-models and Homotopy Algebras