The Einstein-Hilbert action with cosmological constant as a functional of generic form
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Submission date: 10. Oct. 2013
published in: Journal of mathematical physics, 56 (2015) 1, art-no. 012301
DOI number (of the published article): 10.1063/1.4906239
MSC-Numbers: 14D21, 15A66, 53C07, 81T13, 83Cxx
PACS-Numbers: 04.30.-w, 12.10.-g, 12.15._y, 02.65.-p
Keywords and phrases: clifford modules, Dirac operators, Einstein-Hilbert functional, Yang-Mills action, Dirac harmonic maps
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The geometrical underpinnings of a certain class of Dirac operators is discussed. It is demonstrated how these Dirac operators allow to relate various geometric functionals like, for example, the Yang-Mills and the functional of non-linear σ-models (i.e. (Dirac) harmonic maps). In fact, all these functionals are shown to be intimately related to the Einstein-Hilbert action with cosmological constant (EHC). Therefore, the latter may be regarded as a kind of “generic functional”. In addition, the geometrical setup presented also allows to avoid the issue of the “fermion doubling”.