Effective action and heat kernel in a toy model of braneinduced gravity
Abstract
We apply a recently suggested technique of the NeumannDirichlet reduction to a toy model of braneinduced gravity for the calculation of its quantum oneloop effective action. This model is represented by a massive scalar field in the (d+1)dimensional flat bulk supplied with the ddimensional kinetic term localized on a flat brane and mimicking the brane Einstein term of the DvaliGabadadzePorrati (DGP) model. We obtain the inverse mass expansion of the effective action and its ultraviolet divergences which turn out to be nonvanishing for both even and odd spacetime dimensionality d. For the massless case, which corresponds to a limit of the toy DGP model, we obtain the ColemanWeinberg type effective potential of the system. We also obtain the propertime expansion of the heat kernel in this model associated with the generalized Neumann boundary conditions containing secondorder tangential derivatives. We show that in addition to the usual integer and halfinteger powers of the proper time this expansion exhibits, depending on the dimension d, either logarithmic terms or powers multiple of one quarter. This property is considered in the context of strong ellipticity of the boundary value problem, which can be violated when the Euclidean action of the theory is not positive definite.
 Publication:

Physical Review D
 Pub Date:
 February 2007
 DOI:
 10.1103/PhysRevD.75.044010
 arXiv:
 arXiv:hepth/0611326
 Bibcode:
 2007PhRvD..75d4010B
 Keywords:

 04.60.m;
 04.50.+h;
 04.62.+v;
 Quantum gravity;
 Gravity in more than four dimensions KaluzaKlein theory unified field theories;
 alternative theories of gravity;
 Quantum field theory in curved spacetime;
 High Energy Physics  Theory
 EPrint:
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