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

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

2007-08-07

arxiv.org/abs/0708.0955v2

JHEP 0712:098,2007

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 26 pages; typos corrected, references added

Scientific paper

10.1088/1126-6708/2007/12/098

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.

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