1,553 research outputs found
Monodromy Properties of the Energy Momentum Tensor on General Algebraic Curves
A new approach to analyze the properties of the energy-momentum tensor
of conformal field theories on generic Riemann surfaces (RS) is proposed.
is decomposed into components with different monodromy properties,
where is the number of branches in the realization of RS as branch covering
over the complex sphere. This decomposition gives rise to new infinite
dimensional Lie algebra which can be viewed as a generalization of Virasoro
algebra containing information about the global properties of the underlying
RS. In the simplest case of hyperelliptic curves the structure of the algebra
is calculated in two ways and its central extension is explicitly given. The
algebra possess an interesting symmetry with a clear interpretation in the
framework of the radial quantization of CFT's with multivalued fields on the
complex sphere.Comment: 21 pages, plain TeX + harvma
On a selection principle for multivalued semiclassical flows
We study the semiclassical behaviour of solutions of a Schr ̈odinger equation with a scalar po- tential displaying a conical singularity. When a pure state interacts strongly with the singularity of the flow, there are several possible classical evolutions, and it is not known whether the semiclassical limit cor- responds to one of them. Based on recent results, we propose that one of the classical evolutions captures the semiclassical dynamics; moreover, we propose a selection principle for the straightforward calculation of the regularized semiclassical asymptotics. We proceed to investigate numerically the validity of the proposed scheme, by employing a solver based on a posteriori error control for the Schr ̈odinger equation. Thus, for the problems we study, we generate rigorous upper bounds for the error in our asymptotic approximation. For 1-dimensional problems without interference, we obtain compelling agreement between the regularized asymptotics and the full solution. In problems with interference, there is a quantum effect that seems to survive in the classical limit. We discuss the scope of applicability of the proposed regularization approach, and formulate a precise conjecture
A note on generalized hypergeometric functions, KZ solutions, and gluon amplitudes
Some aspects of Aomoto's generalized hypergeometric functions on Grassmannian
spaces are reviewed. Particularly, their integral representations
in terms of twisted homology and cohomology are clarified with an example of
the case which corresponds to Gauss' hypergeometric functions. The
cases of in general lead to -point solutions of the
Knizhnik-Zamolodchikov (KZ) equation. We further analyze the
Schechtman-Varchenko integral representations of the KZ solutions in relation
to the cases. We show that holonomy operators of the so-called
KZ connections can be interpreted as hypergeometric-type integrals. This result
leads to an improved description of a recently proposed holonomy formalism for
gluon amplitudes. We also present a (co)homology interpretation of Grassmannian
formulations for scattering amplitudes in super Yang-Mills
theory.Comment: 51 pages; v2. reference added; v3. minor corrections, published
versio
Dilogarithms, OPE and twisted T-duality
We study the full sigma model with target the three-dimensional Heisenberg
nilmanifold by means of a Hamiltonian formulation of double field theory. We
show that the expected T -duality with the sigma model on a torus endowed with
H-flux is a manifest symmetry of the theory. We compute correlation functions
of scalar fields and show that they exhibit dilogarithmic singularities. We
show how the reflection and pentagonal identities of the dilogarithm can be
interpreted in terms of correlators with 4 and 5 insertions.Comment: 33 page
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
In this paper we develop the Lagrangian and multisymplectic structures of the
Heisenberg magnet (HM) model which are then used as the basis for geometric
discretizations of HM. Despite a topological obstruction to the existence of a
global Lagrangian density, a local variational formulation allows one to derive
local conservation laws using a version of N\"other's theorem from the formal
variational calculus of Gelfand-Dikii. Using the local Lagrangian form we
extend the method of Marsden, Patrick and Schkoller to derive local
multisymplectic discretizations directly from the variational principle. We
employ a version of the finite element method to discretize the space of
sections of the trivial magnetic spin bundle over an
appropriate space-time . Since sections do not form a vector space, the
usual FEM bases can be used only locally with coordinate transformations
intervening on element boundaries, and conservation properties are guaranteed
only within an element. We discuss possible ways of circumventing this problem,
including the use of a local version of the method of characteristics,
non-polynomial FEM bases and Lie-group discretization methods.Comment: 12 pages, accepted Math. and Comp. Simul., May 200
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