222 research outputs found
Geometrically induced magnetic catalysis and critical dimensions
We discuss the combined effect of magnetic fields and geometry in interacting
fermionic systems. At leading order in the heat-kernel expansion, the infrared
singularity (that in flat space leads to the magnetic catalysis) is regulated
by the chiral gap effect, and the catalysis is deactivated by the effect of the
scalar curvature. We discover that an infrared singularity is found in
higher-order terms that mix the magnetic field with curvature, and these lead
to a novel form of geometrically induced magnetic catalysis. The dynamical mass
squared is then modified not only due to the chiral gap effect by an amount
proportional to the curvature, but also by a magnetic shift ,
where represents the number of space-time dimensions. We argue that
is a critical dimension across which the behavior of the magnetic shift changes
qualitatively.Comment: 5 pages; minor change
Casimir energy for de Sitter branes in bulk AdS(5)
The vacuum energy for a massless conformally coupled scalar field in a brane
world set up, corresponding to de Sitter branes in a bulk anti-de Sitter
spacetime, is calculated. We use the Euclidean version of the metric which can
be conformally related to a metric similar in form to the Einstein universe
(S^4 times R). Employing zeta-function regularisation we evaluate the one-loop
effective potential and show that the vacuum energy is zero for the one brane
and non-zero for the two brane configuration. We comment on the back-reaction
of this Casimir energy and on the inclusion of a mass term or non-conformal
coupling.Comment: 6 pages, no figures, references added, typos corrected, to be
published in Phys. Lett.
Zeta Functions in Brane World Cosmology
We present a calculation of the zeta function and of the functional
determinant for a Laplace-type differential operator, corresponding to a scalar
field in a higher dimensional de Sitter brane background, which consists of a
higher dimensional anti-de Sitter bulk spacetime bounded by a de Sitter
section, representing a brane. Contrary to the existing examples, which all
make use of conformal transformations, we evaluate the zeta function working
directly with the higher dimensional wave operator. We also consider a generic
mass term and coupling to curvature, generalizing previous results. The
massless, conformally coupled case is obtained as a limit of the general result
and compared with known calculations. In the limit of large anti-de Sitter
radius, the zeta determinant for the ball is recovered in perfect agreement
with known expressions, providing an interesting check of our result and an
alternative way of obtaining the ball determinant.Comment: 14 pages, 1 figur
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