# 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 »

- 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; 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}

}