Positive mass theorem in extended supergravities. (English) Zbl 1325.83005
Summary: Following the Witten-Nester formalism, we present a useful prescription using Weyl spinors towards the positivity of mass. As a generalization of [the authors, Phys. Rev. D89, No. 2, Article No. 023011, 8 p. (2014: 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-Kähler 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.
MSC:
83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
83C22 | Einstein-Maxwell equations |
83E50 | Supergravity |
83E15 | Kaluza-Klein and other higher-dimensional theories |
83F05 | Relativistic cosmology |
Keywords:
Witten-Nester formalismReferences:
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