40 research outputs found
On Macroscopic Energy Gap for -Quantum Mechanical Systems
The q-deformed harmonic oscillator within the framework of the recently
introduced Schwenk-Wess -Heisenberg algebra is considered. It is shown, that
for "physical" values , the gap between the energy levels decreases
with growing energy. Comparing with the other (real) -deformations of the
harmonic oscillator, where the gap instead increases, indicates that the
formation of the macroscopic energy gap in the Schwenk-Wess -Quantum
Mechanics may be avoided.Comment: 6 pages, TeX, PRA-HEP-92/1
Quantum equivalence of sigma models related by non Abelian Duality Transformations
Coupling constant renormalization is investigated in 2 dimensional sigma
models related by non Abelian duality transformations. In this respect it is
shown that in the one loop order of perturbation theory the duals of a one
parameter family of models, interpolating between the SU(2) principal model and
the O(3) sigma model, exhibit the same behaviour as the original models. For
the O(3) model also the two loop equivalence is investigated, and is found to
be broken just like in the already known example of the principal model.Comment: As a result of the collaboration of new authors the previously
overlooked gauge contribution is inserted into eq.(43) changing not so much
the formulae as part of the conclusion: for the models considered non Abelian
duality is OK in one loo
Regularization of 2d supersymmetric Yang-Mills theory via non commutative geometry
The non commutative geometry is a possible framework to regularize Quantum
Field Theory in a nonperturbative way. This idea is an extension of the lattice
approximation by non commutativity that allows to preserve symmetries. The
supersymmetric version is also studied and more precisely in the case of the
Schwinger model on supersphere [14]. This paper is a generalization of this
latter work to more general gauge groups
'Schwinger Model' on the Fuzzy Sphere
In this paper, we construct a model of spinor fields interacting with
specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this
'Schwinger model'. In constructing the theory of gauge fields interacting with
spinors on fuzzy sphere, we take the approach that the Dirac operator on
q-deformed fuzzy sphere is the gauged Dirac operator on fuzzy
sphere. This introduces interaction between spinors and specific one parameter
family of gauge fields. We also show how to express the field strength for this
gauge field in terms of the Dirac operators and alone. Using the path
integral method, we have calculated the point functions of this model and
show that, in general, they do not vanish, reflecting the chiral non-invariance
of the partition function.Comment: Minor changes, typos corrected, 18 pages, to appear in Mod. Phys.
Lett.
Dual Instantons
We show how to map the Belavin-Polyakov instantons of the O(3)-nonlinear
model to a dual theory where they then appear as nontopological
solitons. They are stationary points of the Euclidean action in the dual
theory, and moreover, the dual action and the O(3)-nonlinear model
action agree on shell.Comment: 13 page
Supersymmetric Quantum Corrections and Poisson-Lie T-Duality
The quantum actions of the (4,4) supersymmetric non-linear sigma model and
its dual in the Abelian case are constructed by using the background superfield
method. The propagators of the quantum superfield and its dual and the gauge
fixing actions of the original and dual (4,4) supersymmetric sigma models are
determined. On the other hand, the BRST transformations are used to obtain the
quantum dual action of the (4,4) supersymmetric non-linear sigma model in the
sense of Poisson-Lie T-dualityComment: 18 page
On dynamical r-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras
According to Etingof and Varchenko, the classical dynamical Yang-Baxter
equation is a guarantee for the consistency of the Poisson bracket on certain
Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these
Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair
\L\subset \A to those on another pair \K\subset \A, where \K\subset
\L\subset \A is a chain of Lie algebras for which \L admits a reductive
decomposition as \L=\K+\M. Several known dynamical r-matrices appear
naturally in this setting, and its application provides new r-matrices, too. In
particular, we exhibit a family of r-matrices for which the dynamical variable
lies in the grade zero subalgebra of an extended affine Lie algebra obtained
from a twisted loop algebra based on an arbitrary finite dimensional self-dual
Lie algebra.Comment: 19 pages, LaTeX, added a reference and a footnote and removed some
typo
A Vector Non-abelian Chern-Simons Duality
Abelian Chern-Simons gauge theory is known to possess a `-self-dual'
action where its coupling constant is inverted {\it i.e.} . Here a vector non-abelian duality is found in the
pure non-abelian Chern-Simons action at the classical level. The dimensional
reduction of the dual Chern-Simons action to two-dimensions constitutes a dual
Wess-Zumino-Witten action already given in the literature.Comment: 14+1 pages, LaTeX file, no figures, version to appear in Phys. Rev
T-duality in the weakly curved background
We consider the closed string propagating in the weakly curved background
which consists of constant metric and Kalb-Ramond field with infinitesimally
small coordinate dependent part. We propose the procedure for constructing the
T-dual theory, performing T-duality transformations along coordinates on which
the Kalb-Ramond field depends. The obtained theory is defined in the
non-geometric double space, described by the Lagrange multiplier and
its -dual . We apply the proposed T-duality procedure to the
T-dual theory and obtain the initial one. We discuss the standard relations
between T-dual theories that the equations of motion and momenta modes of one
theory are the Bianchi identities and the winding modes of the other
Solvable model of strings in a time-dependent plane-wave background
We investigate a string model defined by a special plane-wave metric ds^2 =
2dudv - l(u) x^2 du^2 + dx^2 with l(u) = k/u^2 and k=const > 0. This metric is
a Penrose limit of some cosmological, Dp-brane and fundamental string
backgrounds. Remarkably, in Rosen coordinates the metric has a ``null
cosmology'' interpretation with flat spatial sections and scale factor which is
a power of the light-cone time u. We show that: (i) This spacetime is a
Lorentzian homogeneous space. In particular, like Minkowski space, it admits a
boost isometry in u,v. (ii) It is an exact solution of string theory when
supplemented by a u-dependent dilaton such that its exponent (i.e. effective
string coupling) goes to zero at u=infinity and at the singularity u=0,
reducing back-reaction effects. (iii) The classical string equations in this
background become linear in the light-cone gauge and can be solved explicitly
in terms of Bessel's functions; thus the string model can be directly
quantized. This allows one to address the issue of singularity at the
string-theory level. We examine the propagation of first-quantized
point-particle and string modes in this time-dependent background. Using
certain analytic continuation prescription we argue that string propagation
through the singularity can be smooth.Comment: 58 pages, latex. v2: several references to related previous work
adde