219 research outputs found
Gribov horizon beyond the Landau gauge
Gribov and Zwanziger proposed a modification of Yang-Mills theory in order to
cure the Gribov copy problem. We employ field-dependent BRST transformations to
generalize the Gribov-Zwanziger model from the Landau gauge to general R_xi
gauges. The Gribov horizon functional is presented in explicit form, in both
the non-local and local variants. Finally, we show how to reach any given gauge
from the Landau one.Comment: 1+6 pages; v2: one ref. and 3 clarifications added, published versio
Scattering of Noncommutative Waves and Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
Interactions of noncommutative waves and solitons in 2+1 dimensions can be
analyzed exactly for a supersymmetric and integrable U(n) chiral model
extending the Ward model. Using the Moyal-deformed dressing method in an
antichiral superspace, we construct explicit time-dependent solutions of its
noncommutative field equations by iteratively solving linear equations. The
approach is illustrated by presenting scattering configurations for two
noncommutative U(2) plane waves and for two noncommutative U(2) solitons as
well as by producing a noncommutative U(1) two-soliton bound state.Comment: 1+13 pages; v2: reference added, version published in JHE
Phase transitions and gaps in quantum random energy models
By using a previously established exact characterization of the ground state
of random potential systems in the thermodynamic limit, we determine the ground
and first excited energy levels of quantum random energy models, discrete and
continuous. We rigorously establish the existence of a universal first order
quantum phase transition, obeyed by both the ground and the first excited
states. The presence of an exponentially vanishing minimal gap at the
transition is general but, quite interestingly, the gap averaged over the
realizations of the random potential is finite. This fact leaves still open the
chance for some effective quantum annealing algorithm, not necessarily based on
a quantum adiabatic scheme.Comment: 8 pages, 4 figure
Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model
solitons to generic scalar-field solitons for an infinitely stiff potential.
The static k-lump moduli space C^k/S_k features a natural K"ahler metric
induced from an embedding Grassmannian. The moduli-space dynamics is blind
against adding a WZW-like term to the sigma-model action and thus also applies
to the integrable U(1) Ward model. For the latter's two-soliton motion we
compare the exact field configurations with their supposed moduli-space
approximations. Surprisingly, the two do not match, which questions the
adiabatic method for noncommutative solitons.Comment: 1+15 pages, 2 figures; v2: reference added, to appear in JHE
Noncommutative Moduli for Multi-Instantons
There exists a recursive algorithm for constructing BPST-type
multi-instantons on commutative R^4. When deformed noncommutatively, however,
it becomes difficult to write down non-singular instanton configurations with
topological charge greater than one in explicit form. We circumvent this
difficulty by allowing for the translational instanton moduli to become
noncommutative as well. This makes possible the ADHM construction of 't Hooft
multi-instanton solutions with everywhere self-dual field strengths on
noncommutative R^4.Comment: 1+9 pages; v2: reference added, published versio
Matrix Models and D-branes in Twistor String Theory
We construct two matrix models from twistor string theory: one by dimensional
reduction onto a rational curve and another one by introducing noncommutative
coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment
on the interpretation of our matrix models in terms of topological D-branes and
relate them to a recently proposed string field theory. By extending one of the
models, we can carry over all the ingredients of the super ADHM construction to
a D-brane configuration in the supertwistor space P^(3|4). Eventually, we
present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio
Noncommutative waves have infinite propagation speed
We prove the existence of global solutions to the Cauchy problem for
noncommutative nonlinear wave equations in arbitrary even spatial dimensions
where the noncommutativity is only in the spatial directions. We find that for
existence there are no conditions on the degree of the nonlinearity provided
the potential is positive. We furthermore prove that nonlinear noncommutative
waves have infinite propagation speed, i.e., if the initial conditions at time
0 have a compact support then for any positive time the support of the solution
can be arbitrarily large.Comment: 15 pages, references adde
The sl(2n|2n)^(1) Super-Toda Lattices and the Heavenly Equations as Continuum Limit
The continuum limit of super-Toda models associated with the
affine (super)algebra series produces -dimensional
integrable equations in the spacetimes. The
equations of motion of the (super)Toda hierarchies depend not only on the
chosen (super)algebras but also on the specific presentation of their Cartan
matrices. Four distinct series of integrable hierarchies in relation with
symmetric-versus-antisymmetric, null-versus-nonnull presentations of the
corresponding Cartan matrices are investigated. In the continuum limit we
derive four classes of integrable equations of heavenly type, generalizing the
results previously obtained in the literature. The systems are manifestly N=1
supersymmetric and, for specific choices of the Cartan matrix preserving the
complex structure, admit a hidden N=2 supersymmetry. The coset reduction of the
(super)-heavenly equation to the spacetime (with a line segment) is
illustrated. Finally, integrable supersymmetrically extended models in
dimensions are constructed through dimensional reduction of the
previous systems.Comment: 12 page
- …