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.
Highlights
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 dH
Less studied are the modifications at order R4 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 generalized 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 Courant bracket
Precisely because the gauge fields are built into the definition of the generalized geometry, their Bianchi identities are assumed by construction and any modification of them requires a change in the formalism
Summary
The formalism of generalized geometry has proven to be a very powerful tool to tackle problems in string theory and supergravity. By looking at structures on a generalized tangent space which has “baked in” the much richer gauge field content of these theories, it provides a unified language for the bosonic sector that brings within reach previously intractable problems. We will argue that further considering R4 corrections—which would be highly desirable as it could provide a path to obtain their supersymmetric completion and would have applications to phenomenological models that rely on perturbative effects to fix moduli in flux compactifications—implies again expanding the exceptional generalized geometry, and that the gauge algebra can no longer be captured by a bracket acting just on. We will show that there is an L∞ algebra structure remaining, which we compute explicitly for a particular case
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