47 research outputs found
N=4 Super-Yang-Mills Equations In Harmonic Superspace
We analyze the superfield equations of the 4-dimensional N=4 SYM-theory using
light-cone gauge conditions and the harmonic-superspace approach. The harmonic
superfield equations of motion are drastically simplified in this gauge, in
particular, the basic harmonic-superfield matrices and the corresponding
harmonic analytic gauge connections become nilpotent on-shell.Comment: To be published in Proceedings of the conference "Supersymmetry and
quantum field theory" dedicated to the memory of prof. D.V. Volkov, Kharkov,
July 25-31, 2000; minor corrections include
Quantum N=3, d=3 Chern-Simons Matter Theories in Harmonic Superspace
We develop the background field method for studying classical and quantum
aspects of N=3, d=3 Chern-Simons and matter theories in N=3 harmonic
superspace. As one of the immediate consequences, we prove a nonrenormalization
theorem implying the ultra-violet finiteness of the corresponding supergraph
perturbation theory. We also derive the general hypermultiplet and gauge
superfield propagators in a Chern-Simons background. The leading supergraphs
with two and four external lines are evaluated. In contrast to the
non-supersymmetric theory, the leading quantum correction to the massive
charged hypermultiplet proves to be the super Yang-Mills action rather than the
Chern-Simons one. The hypermultiplet mass is induced by a constant triplet of
central charges in the N=3, d=3 Poincare superalgebra.Comment: 1+37 pages, 3 figures; v2: a reference added, to appear in JHE
Steering between Bloch oscillation and dipole oscillation in parabolic optical waveguide arrays
We study the optical oscillations of supermodes in planar optical waveguide
arrays with parabolically graded propagation constant in individual waveguide
interacting through nearest neighbor couplings. In these arrays, we have
identified a transition between a symmetric dipole oscillation (DO) and a
symmetry-breaking Bloch oscillation (BO) under appropriate conditions. There
exist obvious correspondences between gradon localization and various optical
oscillations. By virtue of an analogue between the oscillation of optical
system and that of a plane pendulum, we propose a shift of the graded profile
to cause a transition from BO to DO. We confirm the optical transition by means
of Hamiltonian optics, as well as by the field evolution of the supermodes. The
results offer great potential applications in optical switching, which can be
applied to design suitable optical devices.Comment: Submitted to JOSA B for publication
N=3 supersymmetric Born-Infeld theory
We construct an off-shell N=3 supersymmetric extension of the abelian D=4
Born-Infeld action starting from the action of supersymmetric Maxwell theory in
N=3 harmonic superspace. A crucial new feature of the N=3 super BI action is
that its interaction part contains only terms of the order 4k in the N=3
superfield strengths. The correct component bosonic BI action arises as the
result of elimination of auxiliary tensor field which is present in the
off-shell N=3 vector multiplet in parallel with the gauge field strength. In
this new Legendre-type representation, the bosonic BI action is fully specified
by a real function of the single variable quartic in the auxiliary tensor
field. The generic choice of this function amounts to a wide set of self-dual
nonlinear extensions of the Maxwell action. All of them admit an off-shell N=3
supersymmetrization.Comment: 18 pages, latex, no figures, slight changes, acknowledgements adde
Renormalizable supersymmetric gauge theory in six dimensions
We construct and discuss a 6D supersymmetric gauge theory involving four
derivatives in the action. The theory involves a dimensionless coupling
constant and is renormalizable. At the tree level, it enjoys N = (1,0)
superconformal symmetry, but the latter is broken by quantum anomaly. Our study
should be considered as preparatory for seeking an extended version of this
theory which would hopefully preserve conformal symmetry at the full quantum
level and be ultraviolet-finite.Comment: 20 pages, 2 figures. An arithmetic error in the calculation of the
coefficient of the beta function is corrected. Its sign (corresponding to the
Landau zero situation) stays the same as in the earlier version
ABJM models in N=3 harmonic superspace
We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena
(ABJM) model in the N=3, d=3 harmonic superspace. In such a formulation three
out of six supersymmetries are realized off shell while the other three mix the
superfields and close on shell. The superfield action involves two
hypermultiplet superfields in the bifundamental representation of the gauge
group and two Chern-Simons gauge superfields corresponding to the left and
right gauge groups. The N=3 superconformal invariance allows only for a minimal
gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar
potential of ABJM emerges after the elimination of auxiliary fields. Besides
the original U(N)xU(N) ABJM model, we also construct N=3 superfield
formulations of some generalizations. For the SU(2)xSU(2) case we give a simple
superfield proof of its enhanced N=8 supersymmetry and SO(8) R-symmetry.Comment: 1+35 pages, minor changes, a reference added, published versio
Superfield Theories in Tensorial Superspaces and the Dynamics of Higher Spin Fields
We present the superfield generalization of free higher spin equations in
tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n)
holonomy as a possible framework for the construction of a non-linear higher
spin field theory. Surprisingly enough, we find that the most general solution
of the supergravity constraints is given by a class of superconformally flat
and OSp(1|n)-related geometries. Because of the conformal symmetry of the
supergravity constraints and of the higher spin field equations such geometries
turn out to be trivial in the sense that they cannot generate a `minimal'
coupling of higher spin fields to their potentials even in curved backgrounds
with a non-zero cosmological constant. This suggests that the construction of
interacting higher spin theories in this framework might require an extension
of the tensorial superspace with additional coordinates such as twistor-like
spinor variables which are used to construct the OSp(1|2n) invariant
(`preonic') superparticle action in tensorial superspace.Comment: LaTeX, 30 pages, no figures. V2. Discussion on conventional
constraints extended, typos corrected, JHEP style, to appear in JHE
Nilpotent deformations of N=2 superspace
We investigate deformations of four-dimensional N=(1,1) euclidean superspace
induced by nonanticommuting fermionic coordinates. We essentially use the
harmonic superspace approach and consider nilpotent bi-differential Poisson
operators only. One variant of such deformations (termed chiral nilpotent)
directly generalizes the recently studied chiral deformation of N=(1/2,1/2)
superspace. It preserves chirality and harmonic analyticity but generically
breaks N=(1,1) to N=(1,0) supersymmetry. Yet, for degenerate choices of the
constant deformation matrix N=(1,1/2) supersymmetry can be retained, i.e. a
fraction of 3/4. An alternative version (termed analytic nilpotent) imposes
minimal nonanticommutativity on the analytic coordinates of harmonic
superspace. It does not affect the analytic subspace and respects all
supersymmetries, at the expense of chirality however. For a chiral nilpotent
deformation, we present non(anti)commutative euclidean analogs of N=2 Maxwell
and hypermultiplet off-shell actions.Comment: 1+16 pages; v2: discussion of (pseudo)conjugations extended, version
to appear in JHE
Scale Invariant Low-Energy Effective Action in N=3 SYM Theory
Using the harmonic superspace approach we study the problem of low-energy
effective action in N=3 SYM theory. The candidate effective action is a scale
and \gamma_5-invariant functional in full N=3 superspace built out of N=3
off-shell superfield strengths. This action is constructed as N=3 superfield
generalization of F^4/\phi^4 component term which is leading in the low-energy
effective action and is simultaneously the first nontrivial term in scale
invariant Born-Infeld action. All higher-order terms in the scale invariant
Born-Infeld action are also shown to admit an off-shell superfield completion
in N=3 harmonic superspace.Comment: 17 pages; v2: typos correcte