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

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Cited by in corpus (16)

• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Double Copy from Homotopy Algebras
• Conformal Field Theory and Algebraic Structure of Gauge Theory
• BV Yang-Mills as a Homotopy Chern-Simons via SFT
• SFT-inspired Algebraic Structures in Gauge Theories
• Quasiclassical Lian-Zuckerman Homotopy Algebras, Courant Algebroids and Gauge Theory
• Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
• Beta-gamma systems and the deformations of the BRST operator
• Metastring Theory and Modular Space-time
• First Order String Theory and the Kodaira-Spencer Equations. I
• First Order String Theory and the Kodaira-Spencer Equations. II
• Homotopy Relations for Topological VOA
• A-infinity structure in string theory and the Yang-Mills equation
• On higher order Leibniz identities in TCFT
• The $L_{\infty }$-algebra of the S-matrix
• Sigma-models and Homotopy Algebras