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Title: Effective action and heat kernel in a toy model of brane-induced gravity

Abstract

We apply a recently suggested technique of the Neumann-Dirichlet reduction to a toy model of brane-induced gravity for the calculation of its quantum one-loop effective action. This model is represented by a massive scalar field in the (d+1)-dimensional flat bulk supplied with the d-dimensional kinetic term localized on a flat brane and mimicking the brane Einstein term of the Dvali-Gabadadze-Porrati (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 Coleman-Weinberg type effective potential of the system. We also obtain the proper-time expansion of the heat kernel in this model associated with the generalized Neumann boundary conditions containing second-order tangential derivatives. We show that in addition to the usual integer and half-integer 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 » definite.« less

Authors:
 [1];  [2];  [3];  [4];  [5];  [1]
  1. Theory Department, Lebedev Physics Institute, Leninsky Prospect 53, Moscow 119991 (Russian Federation)
  2. (Germany)
  3. Dipartimento di Fisica and INFN, via Irnerio 46, 40126 Bologna (Italy)
  4. (Russian Federation)
  5. 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; BOUNDARY-VALUE PROBLEMS; BRANES; COSMOLOGY; EUCLIDEAN SPACE; GRAVITATION; KERNELS; MASS; POTENTIALS; SCALAR FIELDS; SPACE-TIME; 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 brane-induced 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 brane-induced 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 brane-induced gravity". United States. doi:10.1103/PHYSREVD.75.044010.
@article{osti_21011075,
title = {Effective action and heat kernel in a toy model of brane-induced 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 Neumann-Dirichlet reduction to a toy model of brane-induced gravity for the calculation of its quantum one-loop effective action. This model is represented by a massive scalar field in the (d+1)-dimensional flat bulk supplied with the d-dimensional kinetic term localized on a flat brane and mimicking the brane Einstein term of the Dvali-Gabadadze-Porrati (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 Coleman-Weinberg type effective potential of the system. We also obtain the proper-time expansion of the heat kernel in this model associated with the generalized Neumann boundary conditions containing second-order tangential derivatives. We show that in addition to the usual integer and half-integer 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}
}
  • We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in Dvali-Gabadadze-Porrati type scale parameter m, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk M and m. This cutoff M{sub cutoff}={radical}(Mm) is much higher than the analogous strong coupling scale of the Dvali-Gabadadze-Porrati model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of themore » scalar field in the (d+1)-dimensional bulk with the brane carrying the d-dimensional kinetic term of this field. The ultraviolet divergences in this model are obtained for a particular case of d=4.« less
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  • In the present paper a general expression of quantum effective action for arbitrary d-dimensional supergravity is obtained as an expansion on the curvature and its derivatives. The mechanism of inducing Einstein gravity with zero {Lambda} term is proposed. It is shown that the 4-dimensional gravity with the true sign of the Newton constant is induced from d = 5 supergravity when antiperiodic boundary conditions are chosen for all fields of supermultiplet. The one-loop effective action is obtained for d = 4, 5, 7, 10 supergravities with the accuracy of linear curvature terms. The one-loop Viscovisky-De Witt effective action is alsomore » obtained for d = 5 SG's with the accuracy of linear curvature terms.« less