$L_{\infty }$-algebras and membrane sigma models

Abstract

Membrane sigma-models have been used for the systematic description of closed strings in non-geometric flux backgrounds. In particular, the conditions for gauge invariance of the corresponding action functionals were related to the Bianchi identities for the fluxes. In this contribution we demonstrate how to express these Bianchi identities in terms of homotopy relations of the underlying $L_{\infty }$-algebra for the case of the Courant sigma-model. We argue that this result can be utilized in understanding the constraint structure of Double Field Theory and the corresponding membrane sigma-model.

arXiv comment13 pages; contribution to the proceedings of the Humboldt Kolleg Frontiers in Physics: From the Electroweak to the Planck Scales, 15 - 19 September 2019, Corfu, Greece

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