Minimal models of quantum homotopy Lie algebras via the BV-formalism

Abstract

Using the BV-formalism of mathematical physics an explicit construction for the minimal model of a quantum L-infinity-algebra is given as a formal super integral. The approach taken herein to these formal integrals is axiomatic; they can be approached using perturbation theory to obtain combinatorial formulae as shown in the appendix. Additionally, there exists a canonical differential graded Lie algebra morphism mapping formal functions on homology to formal functions on the whole space. An L-infinity-algebra morphism inverse to this differential graded Lie algebra morphism on the level of homology is constructed as a formal super integral.

23 pages. Updated presentation with thanks to Paul Levy, Jim Stasheff, Ted Voronov, and the anonymous referee at JMP

References in corpus (6)

• Deformation theory via differential graded Lie algebras
• Deformation theory and rational homotopy type
• Classes on compactifications of the moduli space of curves through solutions to the quantum master equation
• Koszul duality and homotopy theory of curved Lie algebras
• Operads and moduli spaces
• Unbased rational homotopy theory: a Lie algebra approach

Cited by in corpus (6)

• Quantum $L_{\infty }$ Algebras and the Homological Perturbation Lemma
• Perturbative path-integral of string field and the $A_{\infty }$ structure of the BV master equation
• Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex
• The $L_{\infty }$-algebra of the S-matrix
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Lagrangian Relations and Quantum $L_{\infty }$ Algebras