β–γ systems and the deformations of the BRST operator

• Published in: Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2009-09, Vol.42 (35), p.355401-355401 (12)
• Main Author: Zeitlin, Anton M
• Format: Article
• Language: English
• ISSN: 1751-8121; 1751-8113; 1751-8121
• DOI: 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 quasi-classical 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 a possible algebraic approach to the study of beta-functions in sigma-models.