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arXiv · 1407.3355

Positive mass theorem in extended supergravities

Masato Nozawa·Tetsuya Shiromizu
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Abstract

Following the Witten-Nester formalism, we present a useful prescription using Weyl spinors towards the positivity of mass. As a generalization of arXiv:1310.1663, we show that some "positivity conditions" must be imposed upon the gauge connections appearing in the supercovariant derivative acting on spinors. A complete classification of the connection fulfilling the positivity conditions is given. It turns out that these positivity conditions are indeed satisfied for a number of extended supergravity theories. It is shown that the positivity property holds for the Einstein-complex scalar system, provided that the target space is Hodge-Kahler and the potential is expressed in terms of the superpotential. In the Einstein-Maxwell-dilaton theory with a dilaton potential, the dilaton coupling function and the superpotential are fixed by the positive mass property. We also explore the $N=8$ gauged supergravity and demonstrate that the positivity of the mass holds independently of the gaugings and the deformation parameters.

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Masato Nozawa, Tetsuya Shiromizu. 2014-09-06. Positive mass theorem in extended supergravities. https://doi.org/10.1016/j.nuclphysb.2014.09.002

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