696 research outputs found
Yangian Symmetry in Integrable Quantum Gravity
Dimensional reduction of various gravity and supergravity models leads to
effectively two-dimensional field theories described by gravity coupled G/H
coset space sigma-models. The transition matrices of the associated linear
system provide a complete set of conserved charges. Their Poisson algebra is a
semi-classical Yangian double modified by a twist which is a remnant of the
underlying coset structure. The classical Geroch group is generated by the
Lie-Poisson action of these charges. Canonical quantization of the structure
leads to a twisted Yangian double with fixed central extension at a critical
level.Comment: 23 pages, 1 figure, LaTeX2
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of
dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space
sigma-models coupled to gravity and a dilaton. Using methods developed in the
context of flat space integrable systems, the Wheeler-DeWitt equations for
these models can be reduced to a modified version of the Knizhnik-Zamolodchikov
equations from conformal field theory, the insertions given by singularities in
the spectral parameter plane. This basic result in principle permits the
explicit construction of solutions, i.e. physical states of the quantized
theory. In this way, we arrive at integrable models of quantum gravity with
infinitely many self-interacting propagating degrees of freedom.Comment: 41 pages, 2 figures, Lectures given at NATO Advanced Study Institute
on Quantum Fields and Quantum Space Time, Cargese, France, 22 July - 3 Augus
On the quantization of isomonodromic deformations on the torus
The quantization of isomonodromic deformation of a meromorphic connection on
the torus is shown to lead directly to the Knizhnik-Zamolodchikov-Bernard
equations in the same way as the problem on the sphere leads to the system of
Knizhnik-Zamolodchikov equations. The Poisson bracket required for a
Hamiltonian formulation of isomonodromic deformations is naturally induced by
the Poisson structure of Chern-Simons theory in a holomorphic gauge fixing.
This turns out to be the origin of the appearance of twisted quantities on the
torus.Comment: 13 pages, LaTex2
Measuring the Cosmic Microwave Background Radiation
The Cosmic Microwave Background Radiation (CMBR) has over
the last four decades been measured to increasingly high precision and with that provided information on the early Universe to shape and scrutinize our current cosmological model. Here we provide an overview on the status and prospects of current and future measurements
Generalization of Okamoto's equation to arbitrary Schlesinger systems
The Schlesinger system for the case of four regular singularities
is equivalent to the Painlev\'e VI equation. The Painlev\'e VI equation can in
turn be rewritten in the symmetric form of Okamoto's equation; the dependent
variable in Okamoto's form of the PVI equation is the (slightly transformed)
logarithmic derivative of the Jimbo-Miwa tau-function of the Schlesinger
system. The goal of this note is twofold. First, we find a symmetric uniform
formulation of an arbitrary Schlesinger system with regular singularities in
terms of appropriately defined Virasoro generators. Second, we find analogues
of Okamoto's equation for the case of the Schlesinger system with
an arbitrary number of poles. A new set of scalar equations for the logarithmic
derivatives of the Jimbo-Miwa tau-function is derived in terms of generators of
the Virasoro algebra; these generators are expressed in terms of derivatives
with respect to singularities of the Schlesinger system
Quantization of coset space sigma-models coupled to two-dimensional gravity
The mathematical framework for an exact quantization of the two-dimensional
coset space sigma-models coupled to dilaton gravity, that arise from
dimensional reduction of gravity and supergravity theories, is presented.
Extending previous results the two-time Hamiltonian formulation is obtained,
which describes the complete phase space of the model in the isomonodromic
sector. The Dirac brackets arising from the coset constraints are calculated.
Their quantization allows to relate exact solutions of the corresponding
Wheeler-DeWitt equations to solutions of a modified (Coset)
Knizhnik-Zamolodchikov system. On the classical level, a set of observables is
identified, that is complete for essential sectors of the theory. Quantum
counterparts of these observables and their algebraic structure are
investigated. Their status in alternative quantization procedures is discussed,
employing the link with Hamiltonian Chern-Simons theory.Comment: 46 pages, LaTeX2e, 3 figures, revised version to appear in Commun.
Math. Phy
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom
Schlesinger transformations for elliptic isomonodromic deformations
Schlesinger transformations are discrete monodromy preserving symmetry
transformations of the classical Schlesinger system. Generalizing well-known
results from the Riemann sphere we construct these transformations for
isomonodromic deformations on genus one Riemann surfaces. Their action on the
system's tau-function is computed and we obtain an explicit expression for the
ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2
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