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 positivemore »
 Authors:
 Theory Department, Lebedev Physics Institute, Leninsky Prospect 53, Moscow 119991 (Russian Federation)
 (Germany)
 Dipartimento di Fisica and INFN, via Irnerio 46, 40126 Bologna (Italy)
 (Russian Federation)
 Institut fur Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne (Germany)
 Publication Date:
 OSTI Identifier:
 21011075
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.044010; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; BOUNDARY CONDITIONS; BOUNDARYVALUE PROBLEMS; BRANES; COSMOLOGY; EUCLIDEAN SPACE; GRAVITATION; KERNELS; MASS; POTENTIALS; SCALAR FIELDS; SPACETIME; ULTRAVIOLET DIVERGENCES
Citation Formats
Barvinsky, A. O., Sektion Physik, LMU, Theresienstr. 37, Munich, Kamenshchik, A. Yu., L.D. Landau Institute for Theoretical Physcis of Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow, Kiefer, C., and Nesterov, D. V. Effective action and heat kernel in a toy model of braneinduced gravity. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.044010.
Barvinsky, A. O., Sektion Physik, LMU, Theresienstr. 37, Munich, Kamenshchik, A. Yu., L.D. Landau Institute for Theoretical Physcis of Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow, Kiefer, C., & Nesterov, D. V. Effective action and heat kernel in a toy model of braneinduced gravity. United States. doi:10.1103/PHYSREVD.75.044010.
Barvinsky, A. O., Sektion Physik, LMU, Theresienstr. 37, Munich, Kamenshchik, A. Yu., L.D. Landau Institute for Theoretical Physcis of Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow, Kiefer, C., and Nesterov, D. V. Thu .
"Effective action and heat kernel in a toy model of braneinduced gravity". United States.
doi:10.1103/PHYSREVD.75.044010.
@article{osti_21011075,
title = {Effective action and heat kernel in a toy model of braneinduced gravity},
author = {Barvinsky, A. O. and Sektion Physik, LMU, Theresienstr. 37, Munich and Kamenshchik, A. Yu. and L.D. Landau Institute for Theoretical Physcis of Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow and Kiefer, C. and Nesterov, D. V.},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.75.044010},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

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