Homotopy transfer and L-infinity algebras

Abstract: L-infinity algebras are a generalization of Lie algebras involving,besides a 2-bracket, a potentially infinite number of higher-order brackets which satisfy generalized Jacobi identities. In particular, the usual Jacobi identity for the 2-bracket is violated by terms involving a 3-bracket. Originally discovered in physics in the context of closed string field theory, it has since been understood that an L-infinity algebra can in fact be associated to any classical field theory; the Jacobi identities then encode gauge-invariance of the equations of motion, Noether identities and all that, in a way similar to the BRST-BV field-antifield formalism. In this talk, I will first review the definition of L-infinity algebras, in two complementary ways: 1) the original formulation involving an infinite number of brackets, which can be neatly packaged in a nilpotent coderivation, and 2) the dual picture, where L-infinity relations are encoded in a nilpotent derivation. (For field theories, this derivation is nothing but the BRST-BV differential.) Then, I will explain the mathematical notion of homotopy transfer: how, under certain conditions, the L-infinity structure can descend to a subspace of the original vector space. In the field theory context, this corresponds to the notion of (tree-level) integrating out of degrees of freedom, with the smaller L-infinity algebra encoding the algebraic structure of the effective theory. This is based on work in progress with Alex S. Arvanitakis, Chris Hull and Olaf Hohm.

HEP - theory

Audience: researchers in the topic

Exceptional geometry seminar series

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