73 research outputs found
Surface and flexoelectric polarization in a nematic liquid crystal directly measured by a pyroelectric technique
Effective actions on the squashed three-sphere
The effective actions of a scalar and massless spin-half field are determined
as functions of the deformation of a symmetrically squashed three-sphere. The
extreme oblate case is particularly examined as pertinant to a high temperature
statistical mechanical interpretation that may be relevant for the holographic
principle. Interpreting the squashing parameter as a temperature, we find that
the effective `free energies' on the three-sphere are mixtures of thermal
two-sphere scalars and spinors which, in the case of the spinor on the
three-sphere, have the `wrong' thermal periodicities. However the free energies
do have the same leading high temperature forms as the standard free energies
on the two-sphere. The next few terms in the high-temperature expansion are
also explicitly calculated and briefly compared with the Taub-Bolt-AdS bulk
result.Comment: 23 pages, JyTeX. Conclusion slightly amended, one equation and minor
misprints correcte
Evaluation of Surface and Flexoelectric Polarizations in Nematic Liquid Crystal using Short Pulse Laser Irradiation
The renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime
The renormalization group (RG) is used to study the asymptotically free
-theory in curved spacetime. Several forms of the RG equations for
the effective potential are formulated. By solving these equations we obtain
the one-loop effective potential as well as its explicit forms in the case of
strong gravitational fields and strong scalar fields. Using zeta function
techniques, the one-loop and corresponding RG improved vacuum energies are
found for the Kaluza-Klein backgrounds and . They are given in terms of exponentially convergent series, appropriate
for numerical calculations. A study of these vacuum energies as a function of
compactification lengths and other couplings shows that spontaneous
compactification can be qualitatively different when the RG improved energy is
used.Comment: LaTeX, 15 pages, 4 figure
Spectral analysis and zeta determinant on the deformed spheres
We consider a class of singular Riemannian manifolds, the deformed spheres
, defined as the classical spheres with a one parameter family of
singular Riemannian structures, that reduces for to the classical metric.
After giving explicit formulas for the eigenvalues and eigenfunctions of the
metric Laplacian , we study the associated zeta functions
. We introduce a general method to deal with some
classes of simple and double abstract zeta functions, generalizing the ones
appearing in . An application of this method allows to
obtain the main zeta invariants for these zeta functions in all dimensions, and
in particular and . We give
explicit formulas for the zeta regularized determinant in the low dimensional
cases, , thus generalizing a result of Dowker \cite{Dow1}, and we
compute the first coefficients in the expansion of these determinants in powers
of the deformation parameter .Comment: 1 figur
A Conformally Invariant Holographic Two-Point Function on the Berger Sphere
We apply our previous work on Green's functions for the four-dimensional
quaternionic Taub-NUT manifold to obtain a scalar two-point function on the
homogeneously squashed three-sphere (otherwise known as the Berger sphere),
which lies at its conformal infinity. Using basic notions from conformal
geometry and the theory of boundary value problems, in particular the
Dirichlet-to-Robin operator, we establish that our two-point correlation
function is conformally invariant and corresponds to a boundary operator of
conformal dimension one. It is plausible that the methods we use could have
more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte
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