151 research outputs found
Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
We develop techniques to compute higher loop string amplitudes for twisted
theories with (i.e. the critical case). An important
ingredient is the discovery of an anomaly at every genus in decoupling of BRST
trivial states, captured to all orders by a master anomaly equation. In a
particular realization of the theories, the resulting string field theory
is equivalent to a topological theory in six dimensions, the Kodaira--Spencer
theory, which may be viewed as the closed string analog of the Chern--Simon
theory. Using the mirror map this leads to computation of the `number' of
holomorphic curves of higher genus curves in Calabi--Yau manifolds. It is shown
that topological amplitudes can also be reinterpreted as computing corrections
to superpotential terms appearing in the effective 4d theory resulting from
compactification of standard 10d superstrings on the corresponding
theory. Relations with strings are also pointed out.Comment: 178 pages, 20 figure
FMM-accelerated solvers for the Laplace-Beltrami problem on complex surfaces in three dimensions
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions
arises in many areas of physics, including molecular dynamics (surface
diffusion), electromagnetics (harmonic vector fields), and fluid dynamics
(vesicle deformation). Using classical potential theory,the Laplace-Beltrami
operator can be pre-/post-conditioned with integral operators whose kernel is
translation invariant, resulting in well-conditioned Fredholm integral
equations of the second-kind. These equations have the standard Laplace kernel
from potential theory, and therefore the equations can be solved rapidly and
accurately using a combination of fast multipole methods (FMMs) and high-order
quadrature corrections. In this work we detail such a scheme, presenting two
alternative integral formulations of the Laplace-Beltrami problem, each of
whose solution can be obtained via FMM acceleration. We then present several
applications of the solvers, focusing on the computation of what are known as
harmonic vector fields, relevant for many applications in electromagnetics. A
battery of numerical results are presented for each application, detailing the
performance of the solver in various geometries.Comment: 18 pages, 5 tables, 3 figure
Computation of eigenmodes on a compact hyperbolic 3-space
Measurements of cosmic microwave background (CMB) anisotropy are ideal
experiments for discovering the non-trivial global topology of the universe. To
evaluate the CMB anisotropy in multiply-connected compact cosmological models,
one needs to compute the eigenmodes of the Laplace-Beltrami operator. Using the
direct boundary element method, we numerically obtain the low-lying eigenmodes
on a compact hyperbolic 3-space called the Thurston manifold which is the
second smallest in the known compact hyperbolic 3-manifolds. The computed
eigenmodes are expanded in terms of eigenmodes on the unit three-dimensional
pseudosphere. We numerically find that the expansion coefficients behave as
Gaussian pseudo-random numbers for low-lying eigenmodes. The observed
gaussianity in the CMB fluctuations can partially be attributed to the Gaussian
pseudo-randomness of the expansion coefficients assuming that the Gaussian
pseudo-randomness is the universal property of the compact hyperbolic spaces.Comment: 40 pages, 8 EPS figures; error estimation is included; accepted
Classical and Quantum Gravit
Symbol calculus and zeta--function regularized determinants
In this work, we use semigroup integral to evaluate zeta-function regularized
determinants. This is especially powerful for non--positive operators such as
the Dirac operator. In order to understand fully the quantum effective action
one should know not only the potential term but also the leading kinetic term.
In this purpose we use the Weyl type of symbol calculus to evaluate the
determinant as a derivative expansion. The technique is applied both to a
spin--0 bosonic operator and to the Dirac operator coupled to a scalar field.Comment: Added references, some typos corrected, published versio
Graviton confinement inside hypermonopoles of any dimension
We show the generic existence of metastable massive gravitons in the
four-dimensional core of self-gravitating hypermonopoles in any number of
infinite-volume extra-dimensions. Confinement is observed for Higgs and gauge
bosons couplings of the order unity. Provided these resonances are light
enough, they realise the Dvali-Gabadadze-Porrati mechanism by inducing a
four-dimensional gravity law on some intermediate length scales. The effective
four-dimensional Planck mass is shown to be proportional to a negative power of
the graviton mass. As a result, requiring gravity to be four-dimensional on
cosmological length scales may solve the mass hierarchy problem.Comment: 23 pages, 6 figures, uses iopart. Misprints corrected, references
added, matches published versio
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