35 research outputs found
Non standard parametrizations and adjoint invariants of classical groups
We obtain local parametrizations of classical non-compact Lie groups where
adjoint invariants under maximal compact subgroups are manifest. Extension to
non compact subgroups is straightforward. As a by-product parametrizations of
the same type are obtained for compact groups. They are of physical interest in
any theory gauge invariant under the adjoint action, typical examples being the
two dimensional gauged Wess-Zumino-Witten-Novikov models where these
coordinatizations become of extreme usefulness to get the background fields
representing the vacuum expectation values of the massless modes of the
associated (super) string theory.Comment: 11 pages, latex file, La Plata preprint Th-99/01. Minor changes in
the introduction, version to appear in Physics Letters
A note on the non-commutative Chern-Simons model on manifolds with boundary
We study field theories defined in regions of the spatial non-commutative
(NC) plane with a boundary present delimiting them, concentrating in particular
on the U(1) NC Chern-Simons theory on the upper half plane. We find that
classical consistency and gauge invariance lead necessary to the introduction
of -space of square integrable functions null together with all their
derivatives at the origin. Furthermore the requirement of closure of
under the *-product leads to the introduction of a novel notion of the
*-product itself in regions where a boundary is present, that in turn yields
the complexification of the gauge group and to consider chiral waves in one
sense or other. The canonical quantization of the theory is sketched
identifying the physical states and the physical operators. These last ones
include ordinary NC Wilson lines starting and ending on the boundary that yield
correlation functions depending on points on the one-dimensional boundary. We
finally extend the definition of the *-product to a strip and comment on
possible relevance of these results to finite Quantum Hall systems.Comment: 15 pages, references added, to appear in International Journal of
Modern Physic
Correlation functions in the non-commutative Wess-Zumino-Witten model
We develop a systematic perturbative expansion and compute the one-loop
two-points, three-points and four-points correlation functions in a
non-commutative version of the U(N) Wess-Zumino-Witten model in different
regimes of the -parameter showing in the first case a kind of phase
transition around the value , where is a ultraviolet cut-off in a Schwinger regularization
scheme. As a by-product we obtain the functions of the renormalization group,
showing they are essentially the same as in the commutative case but applied to
the whole U(N) fields; in particular there exists a critical point where they
are null, in agreement with a recent background field computation of the
beta-function, and the anomalous dimension of the Lie algebra-valued field
operator agrees with the current algebra prediction. The non-renormalization of
the level is explicitly verified from the four-points correlator, where a
left-right non-invariant counter-term is needed to render finite the theory,
that it is however null on-shell. These results give support to the equivalence
of this model with the commutative one.Comment: 21 pages, latex, no figures, shortened version to appear in Physics
Letters
SO(3) \times U(1) isometric instantons with non abelian hair in four dimensional string theory
We compute the exact effective string vacuum backgrounds of the level coset model. A compact SU(2) isometry present in this seven
dimensional solution allows to interpreting it after compactification as a four
dimensional non-abelian SU(2) charged instanton with a singular submanifold and
an isometry. The semiclassical backgrounds, solutions of
the type II strings, present similar characteristics.Comment: 12 pages, latex fil
Supertubes and special holonomy
We obtain a -supersymmetric 6-brane solution of IIA Supergravity by
T-dualizing the supertube recently found. The resulting electric
charge is related to the original -brane charge. The uplifted solution to
eleven dimensions results to be a purely geometrical configuration, which can
be interpreted as a bound state of a Taub-NUT space and a pp-wave. Being the
non trivial part of the metric pseudo-Riemannian, the resulting reduced
holonomy group is non-compact and locally isomorphic to a semidirect product of
an Abelian four dimensional group and SU(2).Comment: 11 pages, latex, no figure
On supersymmetric - systems with magnetic fields
We study systems of and branes with non zero world-volume
magnetic fields in the weak coupling limit. We find two configurations for
which the conditions for absence of tachyons in the spectra coincide exactly
with those found in the low energy effective theory approach, for the systems
to preserve 1/8 of the supersymmetries of the Type string theory vacuum.
These conditions give rise to a four-parameter family of solutions in each
case. We present further evidence of the stability of these systems by
computing the lowest order interaction amplitude, verifying the no force
condition as well as the supersymmetric character of the spectrum.Comment: Latex file, no figures, 11 pages, references added, to be published
in Physics Letters
Monopole and Dyon Solutions in AdS space
We consider monopole and dyon classical solutions of the Yang-Mills-Higgs
system coupled to gravity in asymptotically anti-de Sitter space. We discuss
both singular and regular solutions to the second order equations of motion
showing that singular Wu-Yang like dyons can be found, the resulting metric
being of the Reissner-N\"ordstrom type (with cosmological constant). Concerning
regular solutions, we analyze the conditions under which they can be
constructed discussing, for vanishing coupling constant, the main distinctive
features related to the anti-de Sitter asymptotic condition; in particular, we
find in this case that the v.e.v. of the Higgs scalar, ,
should be quantized in units of the natural mass scale (related to
the cosmological constant) according to , with .Comment: 14 pages, latex file, no figure
Exact monopole instantons and cosmological solutions in string theory from abelian dimensional reduction
We compute the exact string vacuum backgrounds corresponding to the
non-compact coset theory . The conformal field theory defined by
the level results in a five dimensional singular solution that
factorizes in an asymptotic region as the linear dilaton solution and a
model. It presents two abelian compact isometries that allow to reinterpreting
it from a four dimensional point of view as a stationary and magnetically
charged space-time resembling in some aspects the Kerr-Newman solution of
general relativity. The theory on the other hand describes a
cosmological solution that interpolates between a singular phase at short times
and a universe after some planckian times.Comment: 18 pages, section 5 replaced by 5 and 6, references added; to appear
in Phys. Rev.
On supersymmetric brane solutions
We analyze in the spirit of hep-th/0110039 the possible existence of
supersymmetric brane systems in flat ten dimensional Minkowski
space. For we show that besides the solutions related by T-duality to
the systems found by Bak and Karch there exist other ansatz
whose compatibility is shown from general arguments and that preserve also
eight supercharges, in particular a system with D2-branes
dissolved on it and Taub-NUT charge. We carry out the explicit construction in
Weyl basis of the corresponding Killing spinors and conjecture the existence of
new solutions for higher dimensional branes with some compact directions
analogous to the supertube recently found.Comment: 12 pages, latex, no figures, to appear in Physics Letters
The fundamental non critical string
We obtain the (super) gravity solution in arbitrary space-time dimension less
than ten, that gives a low energy description of a fundamental string embedded
in a non critical vacuum, product of -dimensional Minkowski space-time and a
cigar-like geometry with scale . This solution, one of the few known
examples of objects doubly localized, both at the origin of the transverse
space as well as at the tip of the cigar, is determined by its charge under
the Kalb-Ramond gauge field , and presumably preserves, for even ,
supercharges. Moreover, we show that the solution is reliable
at least in a region far away from both origins, as it is the case with the
well known branes of critical string theory.Comment: 10 pages, latex file, one figure, to be published in Physics Letters