163 research outputs found
On transversally elliptic operators and the quantization of manifolds with -structure
An -structure on a manifold is an endomorphism field
\phi\in\Gamma(M,\End(TM)) such that . Any -structure
determines an almost CR structure E_{1,0}\subset T_\C M given by the
-eigenbundle of . Using a compatible metric and connection
on , we construct an odd first-order differential operator ,
acting on sections of , whose principal symbol is of the
type considered in arXiv:0810.0338. In the special case of a CR-integrable
almost -structure, we show that when is the generalized
Tanaka-Webster connection of Lotta and Pastore, the operator is given by D
= \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann
operator.
We then describe two "quantizations" of manifolds with -structure that
reduce to familiar methods in symplectic geometry in the case that is a
compatible almost complex structure, and to the contact quantization defined in
\cite{F4} when comes from a contact metric structure. The first is an
index-theoretic approach involving the operator ; for certain group actions
will be transversally elliptic, and using the results in arXiv:0810.0338,
we can give a Riemann-Roch type formula for its index. The second approach uses
an analogue of the polarized sections of a prequantum line bundle, with a CR
structure playing the role of a complex polarization.Comment: 31 page
On higher derivative corrections to Wess-Zumino and Tachyonic actions in type II super string theory
We evaluate in detail the string scattering amplitude to compute different
interactions of two massless scalars, one tachyon and one closed string
Ramond-Ramond field in type II super string theory. In particular we find two
scalar field and two tachyon couplings to all orders of up to
on-shell ambiguity. We then obtain the momentum expansion of this amplitude and
apply this infinite number of couplings to actually check that the infinite
number of tachyon poles of S-matrix element of this amplitude for the
case (where is the spatial dimension of a D-brane and is the rank
of a Ramond-Ramond field strength) to all orders of is precisely
equal to the infinite number of tachyon poles of the field theory. In addition
to confirming the couplings of closed string Ramond-Ramond field to the
world-volume gauge field and scalar fields including commutators, we also
propose an extension of the Wess-Zumino action which naturally reproduces these
new couplings in field theory such that they could be confirmed with direct
S-matrix computations. Finally we show that the infinite number of massless
poles and contact terms of this amplitude for the case can be
reproduced by Chern-Simons, higher derivative corrections of the Wess-Zumino
and symmetrized trace tachyon DBI actions.Comment: 51 pages, some refs and comments added, typos are removed. Almost all
ambiguities in BPS and non-BPS effective actions have been addresse
A Connectivity-Based Eco-Regionalization Method of the Mediterranean Sea
International audienceEcoregionalization of the ocean is a necessary step for spatial management of marine resources. Previous ecoregionalization efforts were based either on the distribution of species or on the distribution of physical and biogeochemical properties. These approaches ignore the dispersal of species by oceanic circulation that can connect regions and isolates others. This dispersal effect can be quantified through connectivity that is the probability, or time of transport between distinct regions. Here a new regionalization method based on a connectivity approach is described and applied to the Mediterranean Sea. This method is based on an ensemble of Lagrangian particle numerical simulations using ocean model outputs at 1/12u resolution. The domain is divided into square subregions of 50 km size. Then particle trajectories are used to quantify the oceanographic distance between each subregions, here defined as the mean connection time. Finally the oceanographic distance matrix is used as a basis for a hierarchical clustering. 22 regions are retained and discussed together with a quantification of the stability of boundaries between regions. Identified regions are generally consistent with the general circulation with boundaries located along current jets or surrounding gyres patterns. Regions are discussed in the light of existing ecoregionalizations and available knowledge on plankton distributions. This objective method complements static regionalization approaches based on the environmental niche concept and can be applied to any oceanic region at any scale
Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex
The locality conditions for the vanishing of local anomalies in field theory
are shown to admit a geometrical interpretation in terms of local equivariant
cohomology, thus providing a method to deal with the problem of locality in the
geometrical approaches to the study of local anomalies based on the
Atiyah-Singer index theorem. The local cohomology is shown to be related to the
cohomology of jet bundles by means of the variational bicomplex theory. Using
these results and the techniques for the computation of the cohomology of
invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology
introduced in [6], we obtain necessary and sufficient conditions for the
cancellation of local gravitational and mixed anomalies.Comment: 36 pages. The paper is divided in two part
A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel
In a rigorous construction of the path integral for supersymmetric quantum
mechanics on a Riemann manifold, based on B\"ar and Pf\"affle's use of
piecewise geodesic paths, the kernel of the time evolution operator is the heat
kernel for the Laplacian on forms. The path integral is approximated by the
integral of a form on the space of piecewise geodesic paths which is the
pullback by a natural section of Mathai and Quillen's Thom form of a bundle
over this space.
In the case of closed paths, the bundle is the tangent space to the space of
geodesic paths, and the integral of this form passes in the limit to the
supertrace of the heat kernel.Comment: 14 pages, LaTeX, no fig
Quantum cohomology of partial flag manifolds
We compute the quantum cohomology rings of the partial flag manifolds
F_{n_1\cdots n_k}=U(n)/(U(n_1)\times \cdots \times U(n_k)). The inductive
computation uses the idea of Givental and Kim. Also we define a notion of the
vertical quantum cohomology ring of the algebraic bundle. For the flag bundle
F_{n_1\cdots n_k}(E) associated with the vector bundle E this ring is found.Comment: 33 page
The -genus and a regularization of an -equivariant Euler class
We show that a new multiplicative genus, in the sense of Hirzebruch, can be
obtained by generalizing a calculation due to Atiyah and Witten. We introduce
this as the -genus, compute its value for some examples and
highlight some of its interesting properties. We also indicate a connection
with the study of multiple zeta values, which gives an algebraic interpretation
for our proposed regularization procedure.Comment: 14 pages; version to appear in J. Phys.
Twisted supersymmetric 5D Yang-Mills theory and contact geometry
We extend the localization calculation of the 3D Chern-Simons partition
function over Seifert manifolds to an analogous calculation in five dimensions.
We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined
on a circle bundle over a four dimensional symplectic manifold. The notion of
contact geometry plays a crucial role in the construction and we suggest a
generalization of the instanton equations to five dimensional contact
manifolds. Our main result is a calculation of the full perturbative partition
function on a five sphere for the twisted supersymmetric Yang-Mills theory with
different Chern-Simons couplings. The final answer is given in terms of a
matrix model. Our construction admits generalizations to higher dimensional
contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov
from the mid 90's, and in a way it is covariantization of their ideas for a
contact manifold.Comment: 28 pages; v2: minor mistake corrected; v3: matches published versio
Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Glueball operators and the microscopic approach to N=1 gauge theories
We explain how to generalize Nekrasov's microscopic approach to N=2 gauge
theories to the N=1 case, focusing on the typical example of the U(N) theory
with one adjoint chiral multiplet X and an arbitrary polynomial tree-level
superpotential Tr W(X). We provide a detailed analysis of the generalized
glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa
matrix model and of the generalized Konishi anomaly equations. We compute in
particular the non-trivial quantum corrections to the Virasoro operators and
algebra that generate these equations. We have performed explicit calculations
up to two instantons, that involve the next-to-leading order corrections in
Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of
references corrected, version to appear in JHE
- âŠ