175 research outputs found
One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity
We present an ansatz for all one-loop amplitudes in pure Einstein gravity for
which the n external gravitons have the same outgoing helicity. These loop
amplitudes, which are rational functions of the momenta, also arise in the
quantization of self-dual gravity in four-dimensional Minkowski space. Our
ansatz agrees with explicit computations via D-dimensional unitarity cuts for n
less than or equal to 6. It also has the expected analytic behavior, for all n,
as a graviton becomes soft, and as two momenta become collinear. The gravity
results are closely related to analogous amplitudes in (self-dual) Yang-Mills
theory.Comment: Latex2e, 13 pages with 2 encapsulated figures. Minor corrections mad
Possible Origin of Fermion Chirality and Gut Structure From Extra Dimensions
The fundamental chiral nature of the observed quarks and leptons and the
emergence of the gauge group itself are most puzzling aspects of the standard
model. Starting from general considerations of topological properties of gauge
field configurations in higher space-time dimensions, it is shown that the
existence of non-trivial structures in ten dimensions would determine a class
of models corresponding to a grand unified GUT structure with complex fermion
representations with respect to . The
discussion is carried out within the framework of string theories with
characteristic energy scales below the Planck mass. Avoidance of topological
obstructions upon continuous deformation of field configurations leads to
global chiral symmetry breaking of the underlying fundamental theory, imposes
rigorous restrictions on the structure of the vacuum and space-time itself and
determines uniquely the gauge structure and matter content.Comment: final version to appear in Phys. Rev.
Symplectic structure of the moduli space of flat connections on a Riemann surface
We consider canonical symplectic structure on the moduli space of flat
{\g}-connections on a Riemann surface of genus with marked points.
For {\g} being a semisimple Lie algebra we obtain an explicit efficient
formula for this symplectic form and prove that it may be represented as a sum
of copies of Kirillov symplectic form on the orbit of dressing
transformations in the Poisson-Lie group and copies of the
symplectic structure on the Heisenberg double of the Poisson-Lie group (the
pair () corresponds to the Lie algebra {\g}).Comment: 20 page
Spectral asymmetry for bag boundary conditions
We give an expression, in terms of boundary spectral functions, for the
spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its
domain is determined by local boundary conditions, and the manifold is of
product type. As an application, we explicitly evaluate the asymmetry in the
case of a finite-length cylinder, and check that the outcome is consistent with
our general result. Finally, we study the asymmetry in a disk, which is a
non-product case, and propose an interpretation.Comment: Some minor changes. To appear in Journal of Physics A: Mathematical
and Genera
The ADHM Construction of Instantons on Noncommutative Spaces
We present an account of the ADHM construction of instantons on Euclidean
space-time from the point of view of noncommutative geometry. We
recall the main ingredients of the classical construction in a coordinate
algebra format, which we then deform using a cocycle twisting procedure to
obtain a method for constructing families of instantons on noncommutative
space-time, parameterised by solutions to an appropriate set of ADHM equations.
We illustrate the noncommutative construction in two special cases: the
Moyal-Groenewold plane and the Connes-Landi plane
.Comment: Latex, 40 page
One-dimensional structures behind twisted and untwisted superYang-Mills theory
We give a one-dimensional interpretation of the four-dimensional twisted N=1
superYang-Mills theory on a Kaehler manifold by performing an appropriate
dimensional reduction. We prove the existence of a 6-generator superalgebra,
which does not possess any invariant Lagrangian but contains two different
subalgebras that determine the twisted and untwisted formulations of the N=1
superYang-Mills theory.Comment: 12 pages. Final version to appear in Lett. Math. Phys. with improved
notation and misprints correcte
Quantum D-branes and exotic smooth R^4
In this paper, we present the idea that the formalism of string theory is
connected with the dimension 4 in a new way, not covered by phenomenological or
model-building approaches. The main connection is given by structures induced
by small exotic smooth R^4's having intrinsic meaning for physics in dimension
4. We extend the notion of stable quantum D-branes in a separable
noncommutative C* algebras over convolution algebras corresponding to the
codimension-1 foliations of S^3 which are mainly connected to small exotic R^4.
The tools of topological K-homology and K-theory as well KK-theory describe
stable quantum branes in the C* algebras when naturally extended to algebras.
In case of convolution algebras, small exotic smooth R^4's embedded in exotic
R^4 correspond to a generalized quantum branes on the algebras. These results
extend the correspondence between exotic R^4 and classical D and NS branes from
our previous work.Comment: 16 pages, no figure, see arXiv/1101.3169 for Part 1 This is part 2 of
the work based on the talk "Small exotic smooth and string
theory" given at the International Congress of Mathematicians, ICM2010,
19-28.08.2010, Hyderabad, Indi
The Aharonov-Bohm effect for massless Dirac fermions and the spectral flow of Dirac type operators with classical boundary conditions
We compute, in topological terms, the spectral flow of an arbitrary family of
self-adjoint Dirac type operators with classical (local) boundary conditions on
a compact Riemannian manifold with boundary under the assumption that the
initial and terminal operators of the family are conjugate by a bundle
automorphism. This result is used to study conditions for the existence of
nonzero spectral flow of a family of self-adjoint Dirac type operators with
local boundary conditions in a two-dimensional domain with nontrivial topology.
Possible physical realizations of nonzero spectral flow are discussed.Comment: 15 pages, 6 figures. Submitted to Theoretical and Mathematical
Physics. v2: A change has been made to the paragraph describing the previous
work of M. Prokhorov
Fake R^4's, Einstein Spaces and Seiberg-Witten Monopole Equations
We discuss the possible relevance of some recent mathematical results and
techniques on four-manifolds to physics. We first suggest that the existence of
uncountably many R^4's with non-equivalent smooth structures, a mathematical
phenomenon unique to four dimensions, may be responsible for the observed
four-dimensionality of spacetime. We then point out the remarkable fact that
self-dual gauge fields and Weyl spinors can live on a manifold of Euclidean
signature without affecting the metric. As a specific example, we consider
solutions of the Seiberg-Witten Monopole Equations in which the U(1) fields are
covariantly constant, the monopole Weyl spinor has only a single constant
component, and the 4-manifold M_4 is a product of two Riemann surfaces
Sigma_{p_1} and Sigma_{p_2}. There are p_{1}-1(p_{2}-1) magnetic(electric)
vortices on \Sigma_{p_1}(\Sigma_{p_2}), with p_1 + p_2 \geq 2 (p_1=p_2= 1 being
excluded). When the two genuses are equal, the electromagnetic fields are
self-dual and one obtains the Einstein space \Sigma_p x \Sigma_p, the monopole
condensate serving as the cosmological constant.Comment: 9 pages, Talk at the Second Gursey Memorial Conference, June 2000,
Istanbu
The chiral anomaly from M theory
We argue that the chiral anomaly of \Ncal = 1 super Yang-Mills theory
admits a dual description as spontaneous symmetry breaking in M theory on
holonomy manifolds. We identify an angle of the background dual to the
anomalous current in field theory. This angle is not an isometry of
the metric and we therefore develop a theory of ``massive isometry'' to
describe fluctuations about such angles. Another example of a massive isometry
occurs in the Atiyah-Hitchin metric.Comment: 1 + 44 pages. LaTe
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