Courant sigma model and \(L_\infty\)-algebras. (English) Zbl 1537.81186
Summary: The Courant sigma model is a 3-dimensional topological sigma model of AKSZ type which has been used for the systematic description of closed strings in non-geometric flux backgrounds. In particular, the expression for the fluxes and their Bianchi identities coincide with the local form of the axioms of a Courant algebroid. On the other hand, the axioms of a Courant algebroid also coincide with the conditions for gauge invariance of the Courant sigma model. In this paper we embed this interplay between background fluxes of closed strings, gauge (or more precisely BRST) symmetries of the Courant sigma model and axioms of a Courant algebroid into an \(L_\infty\)-algebra structure. We show how the complete BV-BRST formulation of the Courant sigma model is described in terms of \(L_\infty\)-algebras. Moreover, the morphism between the \(L_\infty\)-algebra for a Courant algebroid and the one for the corresponding sigma model is constructed.
© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
MSC:
| 81T45 | Topological field theories in quantum mechanics |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
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