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Higher curvature Bianchi identities, generalized geometry, and L∞ algebras

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Coimbra,  Andre
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1907.09501.pdf
(Preprint), 350KB

PhysRevD.100.106001.pdf
(Publisher version), 273KB

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Citation

Coimbra, A. (2019). Higher curvature Bianchi identities, generalized geometry, and L∞ algebras. Physical Review D, 100(10): 106001. doi:10.1103/PhysRevD.100.106001.

Cite as: http://hdl.handle.net/21.11116/0000-0004-76EA-0
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.