Formal Maurer-Cartan Structures: from CFT to Classical Field Equations

Abstract

We show how the well-known classical field equations as Einstein and Yang-Mills ones, which arise as the conformal invariance conditions of certain two-dimensional theories, expanded up to the second order in the formal parameter, can be reformulated as Generalized/formal Maurer-Cartan equations (GMC), where the differential is the BRST operator of String theory. We introduce the bilinear operations which are present in GMC, and study their properties, allowing us to find the symmetries of the resulting equations which will be naturally identified with the diffeomorphism and gauge symmetries of Einstein and Yang-Mills equations correspondingly.

LaTeX2e, 26 pages; typos corrected, references added

References in corpus (2)

• BRST, Generalized Maurer-Cartan Equations and CFT
• Perturbed Beta-Gamma Systems and Complex Geometry

Cited by in corpus (5)

• BV Yang-Mills as a Homotopy Chern-Simons via SFT
• SFT-inspired Algebraic Structures in Gauge Theories
• Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
• Beta-gamma systems and the deformations of the BRST operator
• First Order String Theory and the Kodaira-Spencer Equations. I