78 research outputs found
Antisymmetric tensor fields on spheres: functional determinants and non--local counterterms
The Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields
is considered. Explicit expressions for the spectrum are derived in a quite
direct way, confirming previous results. Associated functional determinants and
the heat kernel expansion are evaluated. Using this method, new non--local
counterterms in the quantum effective action are obtained, which can be
expressed in terms of Betti numbers.Comment: LaTeX, 22 pages, no figure
Abelian duality, walls and boundary conditions in diverse dimensions
We systematically apply the formalism of duality walls to study the action of
duality transformations on boundary conditions and local and nonlocal operators
in two, three, and four-dimensional free field theories. In particular, we
construct a large class of D-branes for two-dimensional sigma-models with
toroidal targets and determine the action of the T-duality group on it. It is
manifest in this formalism that T-duality transformations on D-branes are given
by a differential-geometric version of the Fourier-Mukai transform.Comment: 37 pages, late
Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators
We construct invariant differential operators acting on sections of vector
bundles of densities over a smooth manifold without using a Riemannian metric.
The spectral invariants of such operators are invariant under both the
diffeomorphisms and the gauge transformations and can be used to induce a new
theory of gravitation. It can be viewed as a matrix generalization of Einstein
general relativity that reproduces the standard Einstein theory in the weak
deformation limit. Relations with various mathematical constructions such as
Finsler geometry and Hodge-de Rham theory are discussed.Comment: Version accepted by J. High Energy Phys. Introduction and Discussion
significantly expanded. References added and updated. (41 pages, LaTeX: JHEP3
class, no figures
Renormalized Kaluza-Klein theories
Using six-dimensional quantum electrodynamics () as an example we
study the one-loop renormalization of the theory both from the six and
four-dimensional points of view. Our main conclusion is that the properly
renormalized four dimensional theory never forgets its higher dimensional
origin. In particular, the coefficients of the neccessary extra counterterms in
the four dimensional theory are determined in a precise way. We check our
results by studying the reduction of on a two-torus.Comment: LaTeX, 36 pages. A new section added; references improved, typos
fixe
One loop effective potential in heterotic M-theory
We have calculated the one loop effective potential of the vector multiplets
arising from the compactification to five dimensions of heterotic M-theory on a
Calabi-Yau manifold with h^{1,1}>1. We find that extensive cancellations
between the fermionic and bosonic sectors of the theory cause the effective
potential to vanish, with the exception of a higher order curvature term of the
type which might arise from string corrections.Comment: Latex, 28 pages, 1 figur
Path integral formulation of Hodge duality on the brane
In the warped compactification with a single Randall-Sundrum brane, a
puzzling claim has been made that scalar fields can be bound to the brane but
their Hodge dual higher-rank anti-symmetric tensors cannot. By explicitly
requiring the Hodge duality, a prescription to resolve this puzzle was recently
proposed by Duff and Liu. In this note, we implement the Hodge duality via path
integral formulation in the presence of the background gravity fields of warped
compactifications. It is shown that the prescription of Duff and Liu can be
naturally understood within this framework.Comment: 7 pages, LaTe
Casimir Effect of Graviton and the Entropy Bound
In this note we calculate the Casimir effect of free thermal gravitons in
Einstein universe and discuss how it changes the entropy bound condition
proposed recently by Verlinde [hep-th/0008140] as a higher dimensional
generalization of Cardy's formula for conformal field theories (CFT). We find
that the graviton's Casimir effect is necessary in order not to violate
Verlinde's bound for weakly coupled CFT. We also comment on the implication of
this new Cardy's formula to the thermodynamics of black -brane.Comment: 10 pages; v2. a typo correcte
Eta invariants for flat manifolds
Using H. Donnelly result from the article "Eta Invariants for G-Spaces" we
calculate the eta invariants of the signature operator for almost all
7-dimensional flat manifolds with cyclic holonomy group. In all cases this eta
invariants are an integer numbers. The article was motivated by D. D. Long and
A. Reid article "On the geometric boundaries of hyperbolic 4-manifolds, Geom.
Topology 4, 2000, 171-178Comment: 18 pages, a new version with referees comment
Noncommutative geometry and lower dimensional volumes in Riemannian geometry
In this paper we explain how to define "lower dimensional'' volumes of any
compact Riemannian manifold as the integrals of local Riemannian invariants.
For instance we give sense to the area and the length of such a manifold in any
dimension. Our reasoning is motivated by an idea of Connes and involves in an
essential way noncommutative geometry and the analysis of Dirac operators on
spin manifolds. However, the ultimate definitions of the lower dimensional
volumes don't involve noncommutative geometry or spin structures at all.Comment: 12 page
Heat kernel, effective action and anomalies in noncommutative theories
Being motivated by physical applications (as the phi^4 model) we calculate
the heat kernel coefficients for generalised Laplacians on the Moyal plane
containing both left and right multiplications. We found both star-local and
star-nonlocal terms. By using these results we calculate the large mass and
strong noncommutativity expansion of the effective action and of the vacuum
energy. We also study the axial anomaly in the models with gauge fields acting
on fermions from the left and from the right.Comment: 21 pages, v2: references adde
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