30 research outputs found
D-Branes on C^3_6 part I: prepotential and GW-invariants
This is the first of a set of papers having the aim to provide a detailed
description of brane configurations on a family of noncompact threedimensional
Calabi-Yau manifolds. The starting point is the singular manifold C^3/Z_6,
which admits five distinct crepant resolutions. Here we apply local mirror
symmetry to partially determine the prepotential encoding the GW-invariants of
the resolved varieties. It results that such prepotential provides all numbers
but the ones corresponding to curves having null intersection with the compact
divisor. This is realized by means of a conjecture, due to S. Hosono, so that
our results provide a check confirming at least in part the conjecture.Comment: 66 pages, 18 figures, 15 tables; added reference
Non canonical polarizations of Gravitational Waves
We hereby propose an alternative and additional angle on the nature of
gravitational waves (GWs), postulating the theoretical and experimental
possibility that GWs carry a deformation of the time component of spacetime,
other than the spatial one. By explicitly working outside of the
transverse-traceless gauge, we propose how events with welldefined time
duration, when hit by a GW, would consequently be expected to show a difference
in their characteristic time, as measured from the rest frame of an outside
observer,whose clock is to remain unaffected by the GW. This constitutes a
theoretically viable way in the sense of detecting the passing of the wave
itself and may prove relevant as a standalone method for GWs detection other
than laser interferometers, or as well be implemented as a complementary but
independent system of signal triggering, improving the statistical significance
of existing methods. A simple but physically realistic scenario in which the
appropriate conditions for the generation and detection of GWs with time
dilation are met is presented, along with the conceptual design of an
experimental detector.Comment: 10 pages, 8 figure
A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds
Earlier results show that the N = 1/2 supersymmetric path integral on a
closed even dimensional Riemannian spin manifold (X,g) can be constructed in a
mathematically rigorous way via Chen differential forms and techniques from
non-commutative geometry, if one considers it as a current on the smooth loop
space of X. This construction admits a Duistermaat-Heckman localization
formula. In this note, fixing a topologic spin structure on X, we prove that
any smooth family of Riemannian metrics on X canonically induces a Chern-Simons
current which fits into a transgression formula for the supersymmetric path
integral. In particular, this result entails that the supersymmetric path
integral induces a differential topologic invariant on X, which essentially
stems from the A-hat-genus of X
Banana integrals in configuration space
We reconsider the computation of banana integrals at different loops, by
working in the configuration space, in any dimension. We show how the 2-loop
banana integral can be computed directly from the configuration space
representation, without the need to resort to differential equations, and we
include the analytic extension of the diagram in the space of complex masses.
We also determine explicitly the expansion of the two loop banana
integrals, for , .Comment: 29 pages, several formulas improved, removed a mistak
Perturbative Approach to Analog Hawking Radiation in dielectric media in subcritical regime
We take into account the subcritical case for dielectric media by exploiting
an approximation allowing us to perform perturbative analytical calculations
and still not implying low dispersive effects. We show that in the background
of a specific soliton-like solution, pair-creation occurs and can display a
thermal behaviour governed by an effective temperature. The robustness of the
approach is also corroborated by the analysis of the -model related
to the standard Hopfield model, for which analogous results are obtained.Comment: 22 pages, 6 figure
One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
We apply a definition of generalised super Calabi-Yau variety (SCY) to
supermanifolds of complex dimension one. One of our results is that there are
two SCY's having reduced manifold equal to , namely the
projective super space and the weighted projective super
space . Then we compute the corresponding sheaf
cohomology of superforms, showing that the cohomology with picture number one
is infinite dimensional, while the de Rham cohomology, which is what matters
from a physical point of view, remains finite dimensional. Moreover, we provide
the complete real and holomorphic de Rham cohomology for generic projective
super spaces . We also determine the automorphism groups:
these always match the dimension of the projective super group with the only
exception of , whose automorphism group turns out to be
larger than the projective general linear supergroup. By considering the
cohomology of the super tangent sheaf, we compute the deformations of
, discovering that the presence of a fermionic structure
allows for deformations even if the reduced manifold is rigid. Finally, we show
that is self-mirror, whereas has
a zero dimensional mirror. Also, the mirror map for
naturally endows it with a structure of super Riemann surface.Comment: 50 pages. Accepted for publication in JHE
Genus four superstring measures
A main issue in superstring theory are the superstring measures. D'Hoker and
Phong showed that for genus two these reduce to measures on the moduli space of
curves which are determined by modular forms of weight eight and the bosonic
measure. They also suggested a generalisation to higher genus. We showed that
their approach works, with a minor modification, in genus three and we
announced a positive result also in genus four. Here we give the modular form
in genus four explicitly. Recently S. Grushevsky published this result as part
of a more general approach.Comment: 7 pages. To appear in Letters in Mathematical Physic