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

Anton M. Zeitlin

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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.

Keywords

String Field Theory

Bosonic Strings

BRST Symmetry

 

E-print Number: 0708.0955

Cited: by |

Refers: to

PACS

11.25.Hf Conformal field theory, algebraic structures

11.15.-q Gauge field theories

04.20.Jb Exact solutions

11.25.Sq Nonperturbative techniques; string field theory

Subjects

Gravitation and cosmology

Particle physics and field theory

Dates

Issue 12 (December 2007)

Received 20 November 2007, accepted for publication 18 December 2007

Published 31 December 2007



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