28 research outputs found
Strong Coupling Phenomena on the Noncommutative Plane
We study strong coupling phenomena in U(1) gauge theory on the
non-commutative plane. To do so, we make use of a T-dual description in terms
of an limit of U(N) gauge theory on a commutative torus. The
magnetic flux on this torus is taken to be , while the area scales like
1/N, keeping fixed. With a few assumptions, we argue that the
speed of high frequency light in pure non-commutative QED is modified in the
non-commutative directions by the factor , where
is the non-commutative parameter. If charged flavours are included,
there is an upper bound on the momentum of a photon propagating in the
non-commutative directions, beyond which it is unstable against production of
charged pairs. We also discuss a particular limit of pure
non-commutative QED which is T-dual to a more conventional limit
with fixed. In the non-commutative description, this limit gives rise to
an exotic theory of open strings.Comment: 24 pages, latex, 2 figures, corrected typo in eqn 6.
Wilson line correlators in two-dimensional noncommutative Yang-Mills theory
We study the correlator of two parallel Wilson lines in two-dimensional
noncommutative Yang-Mills theory, following two different approaches. We first
consider a perturbative expansion in the large-N limit and resum all planar
diagrams. The second approach is non-perturbative: we exploit the Morita
equivalence, mapping the two open lines on the noncommutative torus (which
eventually gets decompacted) in two closed Wilson loops winding around the dual
commutative torus. Planarity allows us to single out a suitable region of the
variables involved, where a saddle-point approximation of the general Morita
expression for the correlator can be performed. In this region the correlator
nicely compares with the perturbative result, exhibiting an exponential
increase with respect to the momentum p.Comment: 21 pages, 1 figure, typeset in JHEP style; some formulas corrected in
Sect.3, one reference added, results unchange
Towards an explicit expression of the Seiberg-Witten map at all orders
The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge
theories, and allows to express the noncommutative variables in terms of the
commutative ones. Its explicit form can be found order by order in the
noncommutative parameter theta and the gauge potential A by the requirement
that gauge orbits are mapped on gauge orbits. This of course leaves
ambiguities, corresponding to gauge transformations, and there is an infinity
of solutions. Is there one better, clearer than the others ? In the abelian
case, we were able to find a solution, linked by a gauge transformation to
already known formulas, which has the property of admitting a recursive
formulation, uncovering some pattern in the map. In the special case of a pure
gauge, both abelian and non-abelian, these expressions can be summed up, and
the transformation is expressed using the parametrisation in terms of the gauge
group.Comment: 17 pages. Latex, 1 figure. v2: minor changes, published versio
Comments on the Morita Equivalence
It is known that noncommutative Yang-Mills theory with periodical boundary
conditions on torus at the rational value of the noncommutativity parameter is
Morita equivalent to the ordinary Yang-Mills theory with twisted boundary
conditions on dual torus. We present simple derivation of this fact. We
describe one-to-one correspondence between and gauge invariant observables in
these two theories. In particular, we show that under Morita map Polyakov loops
in the ordinary YM theory go to the open noncommutative Wilson loops discovered
by Ishibashi, Iso, Kawai and Kutazawa.Comment: LaTeX, 10pp. v2: minor typo corrections, references adde
Non-Supersymmetric Attractor Flow in Symmetric Spaces
We derive extremal black hole solutions for a variety of four dimensional
models which, after Kaluza-Klein reduction, admit a description in terms of 3D
gravity coupled to a sigma model with symmetric target space. The solutions are
in correspondence with certain nilpotent generators of the isometry group. In
particular, we provide the exact solution for a non-BPS black hole with generic
charges and asymptotic moduli in N=2 supergravity coupled to one vector
multiplet. Multi-centered solutions can also be generated with this technique.
It is shown that the non-supersymmetric solutions lack the intricate moduli
space of bound configurations that are typical of the supersymmetric case.Comment: 50 pages, 4 figures; v2: Reference added. To appear in JHE
On The Stability of Non-Supersymmetric Attractors in String Theory
We study non-supersymmetric attractors obtained in Type IIA compactifications
on Calabi Yau manifolds. Determining if an attractor is stable or unstable
requires an algebraically complicated analysis in general. We show using group
theoretic techniques that this analysis can be considerably simplified and can
be reduced to solving a simple example like the STU model. For attractors with
D0-D4 brane charges, determining stability requires expanding the effective
potential to quartic order in the massless fields. We obtain the full set of
these terms. For attractors with D0-D6 brane charges, we find that there is a
moduli space of solutions and the resulting attractors are stable. Our analysis
is restricted to the two derivative action.Comment: 20 pages, Late
Separation of Attractors in 1-modulus Quantum Corrected Special Geometry
We study the attractor equations for a quantum corrected prepotential
F=t^3+i\lambda, with \lambda \in R,which is the only correction which preserves
the axion shift symmetry and modifies the geometry.
By performing computations in the ``magnetic'' charge configuration, we find
evidence for interesting phenomena (absent in the classical limit of vanishing
\lambda). For a certain range of the quantum parameter \lambda we find a
``separation'' of attractors, i.e. the existence of multiple solutions to the
Attractor Equations for fixed supporting charge configuration. Furthermore, we
find that, away from the classical limit, a ``transmutation'' of the
supersymmetry-preserving features of the attractors takes place when \lambda
reaches a particular critical value.Comment: 1+24 pages, 11 figures; v2: new section added; v3: change in title,
minor updates, published versio
Strings in Gravimagnetic Fields
We provide a complete solution of closed strings propagating in Nappi-Witten
space. Based on the analysis of geodesics we construct the coherent
wavefunctions which approximate as closely as possible the classical
trajectories. We then present a new free field realization of the current
algebra using the gamma, beta ghost system. Finally we construct the quantum
vertex operators, for the tachyon, by representing the wavefunctions in terms
of the free fields. This allows us to compute the three- and four-point
amplitudes, and propose the general result for N-point tachyon scattering
amplitude.Comment: final version, 29 pages + 4 app
On the Stability of Non-Supersymmetric Quantum Attractors in String Theory
We study four dimensional non-supersymmetric attractors in type IIA string
theory in the presence of sub-leading corrections to the prepotential. For a
given Calabi-Yau manifold, the D0-D4 system admits an attractor point in the
moduli space which is uniquely specified by the black hole charges. The
perturbative corrections to the prepotential do not change the number of
massless directions in the black hole effective potential. We further study
non-supersymmetric D0-D6 black holes in the presence of sub-leading
corrections. In this case the space of attractor points define a hypersurface
in the moduli space.Comment: References Added, Typos Corrected, Appendix A.2 Reordere