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arXiv · 2005.04658

Metric algebroid and Dirac generating operator in Double Field Theory

Ursula Carow-Watamura·Kohei Miura·Satoshi Watamura·Taro Yano
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Abstract

We give a formulation of Double Field Theory (DFT) based on a metric algebroid. We derive a covariant completion of the Bianchi identities, i.e. the pre-Bianchi identity in torsion and an improved generalized curvature, and the pre-Bianchi identity including the dilaton contribution. The derived bracket formulation by the Dirac generating operator is applied to the metric algebroid. We propose a generalized Lichnerowicz formula and show that it is equivalent to the pre-Bianchi identities. The dilaton in this setting is included as an ambiguity in the divergence. The projected generalized Lichnerowicz formula gives a new formulation of the DFT action. The closure of the generalized Lie derivative on the spin bundle yields the Bianchi identities as a consistency condition. A relation to the generalized supergravity equations (GSE) is discussed.

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Ursula Carow-Watamura, Kohei Miura, Satoshi Watamura, Taro Yano. 2020-05-10. Metric algebroid and Dirac generating operator in Double Field Theory. https://doi.org/10.1007/jhep10(2020)192

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