skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
;  [1]
+ Show Author Affiliations
  1. 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.
Copy to clipboard
Barvinsky, A.O., & Nesterov, D.V. Quantum effective action in spacetimes with branes and boundaries. United States. doi:10.1103/PHYSREVD.73.066012.
Copy to clipboard
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.
Copy to clipboard
@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}
}
Copy to clipboard
Journal Article:
DOI:  10.1103/PHYSREVD.73.066012
Other availability
Find in Google Scholar Find in Google Scholar
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

  • - Physical Review. D, Particles Fields
    We construct a gauge-fixing procedure in the path integral for gravitational models with branes and boundaries. This procedure incorporates a set of gauge conditions which gauge away effectively decoupled diffeomorphisms acting in the (d+1)-dimensional bulk and on the d-dimensional brane. The corresponding gauge-fixing factor in the path integral factorizes as a product of the bulk and brane (surface-theory) factors. This factorization underlies a special bulk wave function representation of the brane effective action. We develop the semiclassical expansion for this action and explicitly derive it in the one-loop approximation. The one-loop brane effective action can be decomposed into the summore » of the gauge-fixed bulk contribution and the contribution of the pseudodifferential operator of the brane-to-brane propagation of quantum gravitational perturbations. The gauge dependence of these contributions is analyzed by the method of Ward identities. By the recently suggested method of the Neumann-Dirichlet reduction the bulk propagator in the semiclassical expansion is converted to the Dirichlet boundary conditions preferable from the calculational viewpoint.« less

  • - Physical Review, D (Particles Fields); (United States)
    The functional-differential equation which governs the conformal transformation of the renormalized effective action for a massless, conformally invariant quantized field is solved exactly. The formula so obtained can be used to obtain the effective action in any background spacetime once there exists a conformally related spacetime in which the effective action is known. A simple example is presented to see how our formula is useful to obtain the renormalized stress tensor in the [zeta]-functional regularization scheme.

  • ; ; - Physical Review. D, Particles Fields
    Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent z{>=}1. We continue our earlier work [G. Bertoldi, B. A. Burrington, and A. Peet, preceding Article, Phys. Rev. D 80, 126003 (2009).], exploring the thermodynamic properties of the 'black brane' solutions with horizon topology R{sup 2}. We find that the black branes satisfy the relation E=(2/2+z)Ts where E is the energy density, T is the temperature, and s is the entropy density. This matches the expected behavior for a 2+1 dimensional theorymore » with a scaling symmetry (x{sub 1},x{sub 2}){yields}{lambda}(x{sub 1},x{sub 2}), t{yields}{lambda}{sup z}t.« less

  • ; - Physical Review. D, Particles Fields
    We report a mathematical equivalence between certain models of the Universe relying on domain walls and noncommutative geometries. It is shown that a two-braneworld made of two domain walls can be seen as a 'noncommutative' two-sheeted spacetime under certain assumptions. This equivalence also implies a model-independent phenomenology, which is presently studied. Matter swapping between the two branes (or sheets) is predicted through fermionic oscillations induced by magnetic vector potentials. This phenomenon, which might be experimentally studied, could reveal the existence of extra dimensions in a new and accessible way.

  • ; - J. Math. Phys. (N.Y.), v. 16, no. 3, pp. 485-492