Finite-temperature Casimir effect in Randall–Sundrum models

Abstract

The finite temperature Casimir effect for a scalar field in the bulk region of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation a on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attractiveness versus repulsiveness of the temperature correction to the force is discussed in the typical special cases of Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is made use of, as this turns out to be most convenient. Some comments are made on the related contemporary literature.

Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

“…When evaluating the QED effective lagrangian at finite temperature, the time component of the momentum four vector, over which we integrate, takes on only discrete values for a fixed temperature, while when computing the Casimir energy, an analogous substitution takes place in a space component of the momentum vector for a fixed distance between the plates. Recently there has been much interest [24][25][26] in studying the finite temperature Casimir effect in higher dimensional space-time models with compactified extra dimensions, like the Randall-Sundrum models [27,28]. A literature search reveals that the effective lagrangian in a background magnetic field at finite temperature and density has been studied within the framework of QED [10][11][12]18], or within the framework of the electroweak model but prior to the breaking of the electroweak symmetry, when the magnetic fields that are present belong to the U(1) group of hypercharge and hence are called hypermagnetic fields [29][30][31].…”

Gluing Formula for Casimir Energies

“…In order to control these divergencies, different regularization techniques have been applied [4,5,8,14,16,17,29,35,40]. However, they typically lead to different divergencies which raises the question of their interpretation.…”

“…Many configurations, such as flat pistons at zero temperature [11][12][13][14][15][16][17][18][19][20] or finite temperatures [21][22][23][24], as well as curved pistons [25][26][27][28][29], have been analyzed on the basis of the spectrum of a Laplace-type operator associated with M 1 and M 2 . It is the aim of this article to introduce a completely new perspective on this type of analysis.…”

The Casimir Effect at Finite Temperature in a Six-Dimensional Vortex Scenario

“…The Casimir energy for a rectangular cavity including thermal corrections was considered and the temperature controls the energy sign [56]. The Casimir effect for a scalar field within two parallel plates under thermal influence in the bulk region of Randall-Sundrum models was also evaluated [57,58]. In addition, the thermal modification to the Casimir effect for parallel plates involving massless Majorana fermions was analyzed [59].…”