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arXiv · 1907.09501

Higher curvature Bianchi identities, generalised geometry and $L_{\infty}$ algebras

André Coimbra
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Abstract

The Bianchi identities for bosonic fluxes in supergravity can receive higher derivative quantum and string corrections, the most well known being that of Heterotic theory $d H = \tfrac{1}{4}\alpha'(\text{tr } F^2 - \text{tr } R^2)$. Less studied are the modifications at order $R^4$ that may arise, for example, in the Bianchi identity for the seven-form flux of M theory compactifications. We argue that such corrections appear to be incompatible with the exceptional generalised geometry description of the lower order supergravity, and seem to imply a gauge algebra for the bosonic potentials that cannot be written in terms of an (exceptional) Courant bracket. However, we show that this algebra retains the form of an $L_{\infty}$ gauge field theory, which terminates at a level ten multibracket for the case involving just the seven-form flux.

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André Coimbra. 2019-07-22. Higher curvature Bianchi identities, generalised geometry and $L_{\infty}$ algebras. https://doi.org/10.1103/physrevd.100.106001

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