95 research outputs found
Affine Poisson and affine quasi-Poisson T-duality
We generalize the Poisson-Lie T-duality by making use of the structure of the
affine Poisson group which is the concept introduced some time ago in Poisson
geometry as a generalization of the Poisson-Lie group. We also introduce a new
notion of an affine quasi-Poisson group and show that it gives rise to a still
more general T-duality framework. We establish for a class of examples that
this new T-duality is compatible with the renormalization group flow.Comment: 36 pages, Section 7 is added which explains the relations of the
affine (quasi-)Poisson T-duality to the theory of dressing cosets, there are
some stylistic improvements also in other section
Gauge theories on the noncommutative sphere
Gauge theories are formulated on the noncommutative two-sphere. These
theories have only finite number of degrees of freedom, nevertheless they
exhibit both the gauge symmetry and the SU(2) "Poincar\'e" symmetry of the
sphere. In particular, the coupling of gauge fields to chiral fermions is
naturally achieved.Comment: 33 pages, LaTe
A nonperturbative regularization of the supersymmetric Schwinger model
It is shown that noncommutative geometry is a nonperturbative regulator which
can manifestly preserve a space supersymmetry and a supergauge symmetry while
keeping only a finite number of degrees of freedom in a theory. The simplest
N=1 case of an U(1) supergauge theory on the sphere is worked out in detail.Comment: 29 pages, LaTe
The formulae of Kontsevich and Verlinde from the perspective of the Drinfeld double
A two dimensional gauge theory is canonically associated to every Drinfeld
double. For particular doubles, the theory turns out to be e.g. the ordinary
Yang-Mills theory, the G/G gauged WZNW model or the Poisson -model that
underlies the Kontsevich quantization formula. We calculate the arbitrary genus
partition function of the latter. The result is the -deformation of the
ordinary Yang-Mills partition function in the sense that the series over the
weights is replaced by the same series over the -weights. For equal to a
root of unity the series acquires the affine Weyl symmetry and its truncation
to the alcove coincides with the Verlinde formula.Comment: 36 pages, LaTeX, references adde
An extended fuzzy supersphere and twisted chiral superfields
A noncommutative associative algebra of N=2 fuzzy supersphere is introduced.
It turns out to possess a nontrivial automorphism which relates twisted chiral
to twisted anti-chiral superfields and hence makes possible to construct
noncommutative nonlinear \si-models with extended supersymmetry.Comment: 20 pages, LaTe
Poisson-Lie T-duals of the bi-Yang-Baxter models
We prove the conjecture of Sfetsos, Siampos and Thompson that suitable
analytic continuations of the Poisson-Lie T-duals of the bi-Yang-Baxter sigma
models coincide with the recently introduced generalized lambda models. We then
generalize this result by showing that the analytic continuation of a generic
sigma model of "universal WZW-type" introduced by Tseytlin in 1993 is nothing
but the Poisson-Lie T-dual of a generic Poisson-Lie symmetric sigma model
introduced by Klimcik and Severa in 1995.Comment: 15 pages, we present an additional result that the analytic
continuation of a generic sigma model of "universal WZW-type" introduced by
Tseytlin in 1993 is nothing but the Poisson-Lie T-dual of a generic
Poisson-Lie symmetric sigma model introduced by Klimcik and Severa in 199
- …