# Quantum effective action in spacetimes with branes and boundaries

## Abstract

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree-level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane--the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in the heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest-order surface terms in the case of Robin and oblique boundary onditions. We briefly discuss multiloop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background-field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.

- Authors:

- Theory Department, Lebedev Physics Institute, Leninsky Prospect 53, Moscow 119991 (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 20782711

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.066012; (c) 2006 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; APPROXIMATIONS; BOUNDARY CONDITIONS; DIRICHLET PROBLEM; DUALITY; MEMBRANES; PROPAGATOR; QUANTUM GRAVITY; SPACE-TIME; SURFACES

### Citation Formats

```
Barvinsky, A.O., and Nesterov, D.V.
```*Quantum effective action in spacetimes with branes and boundaries*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.066012.

```
Barvinsky, A.O., & Nesterov, D.V.
```*Quantum effective action in spacetimes with branes and boundaries*. United States. doi:10.1103/PHYSREVD.73.066012.

```
Barvinsky, A.O., and Nesterov, D.V. Wed .
"Quantum effective action in spacetimes with branes and boundaries". United States.
doi:10.1103/PHYSREVD.73.066012.
```

```
@article{osti_20782711,
```

title = {Quantum effective action in spacetimes with branes and boundaries},

author = {Barvinsky, A.O. and Nesterov, D.V.},

abstractNote = {We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree-level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane--the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in the heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest-order surface terms in the case of Robin and oblique boundary onditions. We briefly discuss multiloop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background-field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.},

doi = {10.1103/PHYSREVD.73.066012},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}