31 research outputs found
On supermatrix models, Poisson geometry and noncommutative supersymmetric gauge theories
We construct a new supermatrix model which represents a manifestly
supersymmetric noncommutative regularisation of the
supersymmetric Schwinger model on the supersphere. Our construction is much
simpler than those already existing in the literature and it was found by using
Poisson geometry in a substantial way.Comment: 29 pages, we enlarge Section 3.3 by adding a comparison with older
results on the subject of the component expansion
Hidden isometry of "T-duality without isometry"
We study the T-dualisability criteria of Chatzistavrakidis, Deser and Jonke
[3] who recently used Lie algebroid gauge theories to obtain sigma models
exhibiting a "T-duality without isometry". We point out that those
T-dualisability criteria are not written invariantly in [3] and depend on the
choice of the algebroid framing. We then show that there always exists an
isometric framing for which the Lie algebroid gauging boils down to standard
Yang-Mills gauging. The "T-duality without isometry" of Chatzistavrakidis,
Deser and Jonke is therefore nothing but traditional isometric non-Abelian
T-duality in disguise.Comment: 15 page
Quasitriangular chiral WZW model in a nutshell
We give the bare-bone description of the quasitriangular chiral WZW model for
the particular choice of the Lu-Weinstein-Soibelman Drinfeld double of the
affine Kac-Moody group. The symplectic structure of the model and its
Poisson-Lie symmetry are completely characterized by two -matrices with
spectral parameter. One of them is ordinary and trigonometric and characterizes
the -current algebra. The other is dynamical and elliptic (in fact Felder's
one) and characterizes the braiding of -primary fields.Comment: 8 pages, LaTeX, to appear in the Proceedings of the Yokohama meeting
on String theory and noncommutative geometry (March 2001
q-deformation of
We construct the action of the quantum double of \uq on the standard
Podle\'s sphere and interpret it as the quantum projective formula generalizing
to the q-deformed setting the action of the Lorentz group of global conformal
transformations on the ordinary Riemann sphere.Comment: LaTeX, 16 pages, we add a reference where an alternative construction
of the q-Lorentz group action on the Podles sphere is give
D-branes in the Euclidean and T-duality
We show that D-branes in the Euclidean can be naturally associated to
the maximally isotropic subgroups of the Lu-Weinstein double of SU(2). This
picture makes very transparent the residual loop group symmetry of the D-brane
configurations and gives also immediately the D-branes shapes and the
-model boundary conditions in the de Sitter T-dual of the
WZW model.Comment: 29 pages, LaTeX, references adde
One loop renormalizability of the Poisson-Lie sigma models
We present the proof of the one loop renormalizability in the strict field
theoretic sense of the Poisson-Lie sigma models. The result is valid for any
Drinfeld double and it relies solely on the Poisson-Lie structure encoded in
the target manifold.Comment: 11 page
Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction
The trigonometric Ruijsenaars-Schneider model is derived by symplectic
reduction of Poisson-Lie symmetric free motion on the group U(n). The commuting
flows of the model are effortlessly obtained by reducing canonical free flows
on the Heisenberg double of U(n). The free flows are associated with a very
simple Lax matrix, which is shown to yield the Ruijsenaars-Schneider Lax matrix
upon reduction.Comment: 13 pages, LaTeX, minor modifications and references added in v
Quantum Fluctuations and Curvature Singularities in Jackiw-Teitelboim Gravity
The Jackiw-Teitelboim gravity with the matter degrees of freedom is
considered. The classical model is exactly solvable and its solutions describe
non-trivial gravitational scattering of matter wave-packets. For huge amount of
the solutions the scattering space-times are free of curvature singularities.
However, the quantum corrections to the field equations inevitably cause the
formation of (thunderbolt) curvature singularities, vanishing only in the limit
. The singularities cut the space-time and disallow propagation to
the future.The model is inspired by the dimensional reduction of 4-d pure
Einstein gravity, restricted to the space-times with two commuting space-like
Killing vectors. The matter degrees of freedom also stem from the 4-d ansatz.
The measures for the continual integrations are judiciously chosen and one loop
contributions (including the graviton and the dilaton ones) are evaluated. For
the number of the matter fields we obtain even the exact effective
action, applying the DDK-procedure. The effective action is nonlocal, but the
semiclassical equations can be solved by using some theory of the Hankel
transformations.Comment: 32 pages, LaTeX, PRA-HEP-93/