308 research outputs found
Covariant quantization of N=1/2 SYM theories and supergauge invariance
So far, quantum properties of N=1/2 nonanticommutative (NAC) super
Yang--Mills theories have been investigated in the WZ gauge. The gauge
independence of the results requires assuming that at the quantum level
supergauge invariance is not broken by nonanticommutative geometry. In this
paper we use an alternative approach which allows studying these theories in a
manifestly gauge independent superspace setup. This is accomplished by
generalizing the background field method to the NAC case, by moving to a
momentum superspace where star products are treated as exponential factors and
by developing momentum supergraph techniques. We compute the one--loop gauge
effective action for NAC U(N) gauge theories with matter in the adjoint
representation. Despite the appearance of divergent contributions which break
(super)gauge invariance, we prove that the effective action at this order is
indeed invariant.Comment: 24 pages, 3 figures, some references adde
Plane waves from double extended spacetimes
We study exact string backgrounds (WZW models) generated by nonsemisimple
algebras which are obtained as double extensions of generic D--dimensional
semisimple algebras. We prove that a suitable change of coordinates always
exists which reduces these backgrounds to be the product of the nontrivial
background associated to the original algebra and two dimensional Minkowski.
However, under suitable contraction, the algebra reduces to a Nappi--Witten
algebra and the corresponding spacetime geometry, no more factorized, can be
interpreted as the Penrose limit of the original background. For both
configurations we construct D--brane solutions and prove that {\em all} the
branes survive the Penrose limit. Therefore, the limit procedure can be used to
extract informations about Nappi--Witten plane wave backgrounds in arbitrary
dimensions.Comment: 27 pages, no figures, references adde
Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are
approximated by equations of the discrete nonlinear Schrodinger type. We show
how to justify this approximation by two methods, which have been very popular
in the recent literature. The first method relies on a priori energy estimates
and multi-scale decompositions. The second method is based on a resonant normal
form theorem. We show that although the two methods are different in the
implementation, they produce equivalent results as the end product. We also
discuss applications of the discrete nonlinear Schrodinger equation in the
context of existence and stability of breathers of the Klein--Gordon lattice
Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices
We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite
lattices. We also show that the breathers are well approximated by the ground
state of the nonlinear Schroedinger equation. The result is obtained by
exploiting the relation between the Klein Gordon lattice and the discrete Non
Linear Schroedinger lattice. The proof is based on a Lyapunov-Schmidt
decomposition and continuum approximation techniques introduced in [7],
actually using its main result as an important lemma
On duality and reflection factors for the sinh-Gordon model
The sinh-Gordon model with integrable boundary conditions is considered in
low order perturbation theory. It is pointed out that results obtained by
Ghoshal for the sine-Gordon breather reflection factors suggest an interesting
dual relationship between models with different boundary conditions. Ghoshal's
formula for the lightest breather is checked perturbatively to in
the special set of cases in which the symmetry is maintained.
It is noted that the parametrisation of the boundary potential which is natural
for the semi-classical approximation also provides a good parametrisation at
the `free-fermion' point.Comment: 17 pages, harvmac(b
Exact results in planar N=1 superconformal Yang-Mills theory
In the \beta-deformed N=4 supersymmetric SU(N) Yang-Mills theory we study the
class of operators O_J = Tr(\Phi_i^J \Phi_k), i\neq k and compute their exact
anomalous dimensions for N,J\to\infty. This leads to a prediction for the
masses of the corresponding states in the dual string theory sector. We test
the exact formula perturbatively up to two loops. The consistency of the
perturbative calculation with the exact result indicates that in the planar
limit the one--loop condition g^2=h\bar{h} for superconformal invariance is
indeed sufficient to insure the {\em exact} superconformal invariance of the
theory. We present a direct proof of this point in perturbation theory. The O_J
sector of this theory shares many similarities with the BMN sector of the N=4
theory in the large R--charge limit.Comment: LaTex, 14 pages, 3 figures; v2: minor corrections and one reference
adde
Light-like Wilson loops in ABJM and maximal transcendentality
We revisit the computation of the two-loop light-like tetragonal Wilson loop
for three dimensional pure Chern-Simons and N=6 Chern-Simons-matter theory,
within dimensional regularization with dimensional reduction scheme. Our
examination shows that, contrary to prior belief, the result respects maximal
transcendentality as is the case of the four-point scattering amplitude of the
theory. Remarkably, the corrected result matches exactly the scattering
amplitude both in the divergent and in the finite parts, constants included.Comment: 11 page
The 1/2 BPS Wilson loop in ABJ(M) at two loops: The details
We compute the expectation value of the 1/2 BPS circular Wilson loop operator
in ABJ(M) theory at two loops in perturbation theory. Our result turns out to
be in exact agreement with the weak coupling limit of the prediction coming
from localization, including finite N contributions associated to non-planar
diagrams. It also confirms the identification of the correct framing factor
that connects framing-zero and framing-one expressions, previously proposed.
The evaluation of the 1/2 BPS operator is made technically difficult in
comparison with other observables of ABJ(M) theory by the appearance of
integrals involving the coupling between fermions and gauge fields, which are
absent for instance in the 1/6 BPS case. We describe in detail how to
analytically solve these integrals in dimensional regularization with
dimensional reduction (DRED). By suitably performing the physical limit to
three dimensions we clarify the role played by short distance divergences on
the final result and the mechanism of their cancellation.Comment: 54 pages, 2 figure
Hamiltonian lattice dynamics
Hamiltonian lattice dynamics is a very active and relevant field of research. In this Special Issue, by means of some recent results by leading experts in the field, we tried to illustrate how broad and rich it can be, and how it can be seen as excellent playground for Mathematics in Engineering
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