479 research outputs found
Nondiffracting Accelerating Waves: Weber waves and parabolic momentum
Diffraction is one of the universal phenomena of physics, and a way to
overcome it has always represented a challenge for physicists. In order to
control diffraction, the study of structured waves has become decisive. Here,
we present a specific class of nondiffracting spatially accelerating solutions
of the Maxwell equations: the Weber waves. These nonparaxial waves propagate
along parabolic trajectories while approximately preserving their shape. They
are expressed in an analytic closed form and naturally separate in forward and
backward propagation. We show that the Weber waves are self-healing, can form
periodic breather waves and have a well-defined conserved quantity: the
parabolic momentum. We find that our Weber waves for moderate to large values
of the parabolic momenta can be described by a modulated Airy function. Because
the Weber waves are exact time-harmonic solutions of the wave equation, they
have implications for many linear wave systems in nature, ranging from
acoustic, electromagnetic and elastic waves to surface waves in fluids and
membranes.Comment: 10 pages, 4 figures, v2: minor typos correcte
Observation of accelerating parabolic beams
We report the first observation of accelerating parabolic beams. These accelerating parabolic beams are similar to the Airy beams because they exhibit the unusual ability to remain diffraction-free while having a quadratic transverse shift during propagation. The amplitude and phase masks required to generate these beams are encoded onto a single liquid crystal display. Experimental results agree well with theory
Interpreting the M2-brane Action
The world-volume theory of multiple M2-branes proposed recently has a free
scalar field. For large vev of this scalar field the world-volume action
reduces to that of multiple D2-branes with Yang-Mills coupling proportional to
the vev. We suggest that the correct interpretation of this scalar field is as
the radial position of the M2-brane center of mass in a cylindrical polar
coordinate system. Regarding the azimuthal angle as compact we can regard this
as a set of coincident D2-branes in type IIA string theory with varying dilaton
and metric. We find that the effective world-volume theory on the D2-branes has
Yang-Mills coupling proportional to the radial coordinate; furthermore the
radial coordinate satisfies free field equations of motion. This agrees with
the corresponding results derived from the M2-brane world-volume theory.Comment: LaTeX file, 6 page
Light-cone analysis of ungauged and topologically gauged BLG theories
We consider three-dimensional maximally superconformal
Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version
(constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge.
After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory
looks more conventional and, apart from the order of the interaction terms,
resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone
superspace version of the BLG theory is given to quadratic and quartic order
and some problems with constructing the sixth order interaction terms are
discussed. In the topologically gauged case, we analyze the field equations
related to the three Chern-Simons type terms of N=8 conformal supergravity and
discuss some of the special features of this theory and its couplings to BLG.Comment: 22 pages; v2 some typos correcte
On the Problem of Multiple M2 Branes
A simplified version of 3d BL theory is considered, which allows any number N
of M2 branes in d=11. The underlying 3-algebra structure is provided by
degenerate U(N) Nambu bracket [X,Y,Z] = tr(X) [Y,Z] + tr(Y) [Z,X] + tr(Z)
[X,Y], the corresponding f^{abcd} is not totally antisymmetric and extended
supersymmetry of the action remains to be checked. All the fields, including
auxiliary non-propagating gauge fields, are in adjoint representation of SU(N)
and the only remnant of 3-algebra structure is an octuple of gauge singlets,
acquiring vacuum expectation value in transition to D2 branes in d=10.Comment: 12 page
Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model
Basing upon experience from performing double-dimensional reduction of the
D=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 x
CP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishing
condition of the contribution to the D=11 supervielbein components tangent to
D=10 space-time proportional to the differential of the coordinate
parametrizing compact 11-th space-time dimension, that is identified with the
supermembrane world-volume compact dimension. For AdS_4 x S^7 supermembrane
Kaluza-Klein gauge removes half Grassmann coordinates associated with 8
space-time supersymmetries, broken by the AdS_4 x CP^3 superbackground, by
imposing D=3 (anti-)Majorana condition on them. The consideration relies on the
realization of osp(4|8) isometry superalgebra of the AdS_4 x S^7
superbackground as D=3 N=8 superconformal algebra. Requiring further vanishing
of the D=10 dilaton leaves in the sector of broken supersymmetries just two
Grassmann coordinates organized into D=3 (anti-)Majorana spinor that defines
minimal SL(2,R)-covariant extension of the OSp(4|6)/(SO(1,3)x U(3))
sigma-model. Among 4 possibilities of such a minimal extension we consider in
detail one, that corresponds to picking out D=3 Majorana coordinate related to
broken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstring
equations of motion in this partial kappa-symmetry gauge are integrable. Also
the relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 x
CP^3 superstring is revisited.Comment: LaTeX, 22 pages; v2: minor improvements in the text, typos corrected,
references adde
Super-Yang-Mills and M5-branes
We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge
theory with the help of a space-like constant vector , whose norm
determines the Yang-Mills coupling constant. After the localization of
the 6D gauge theory acquires Lorentzian invariance as well as scale invariance.
We discuss KK states, instantons and the flux quantization. The 6D theory
admits extended solutions like 1/2 BPS `strings' and monopoles.Comment: 15 pages; minor changes, to appear in JHE
M-Theory in the Gaugeon Formalism
In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena (ABJM)
theory in superspace formalism. We then study the quantum gauge
transformations for this ABJM theory in gaugeon formalism. We will also analyse
the extended BRST symmetry for this ABJM theory in gaugeon formalism and show
that these BRST transformations for this theory are nilpotent and this in turn
leads to the unitary evolution of the -matrix.Comment: 8 pages, 0 figures, accepted for publication in Comm. Theor. Phy
AdS_4/CFT_3 -- Squashed, Stretched and Warped
We use group theoretic methods to calculate the spectrum of short multiplets
around the extremum of N=8 gauged supergravity potential which possesses N=2
supersymmetry and SU(3) global symmetry. Upon uplifting to M-theory, it
describes a warped product of AdS_4 and a certain squashed and stretched
7-sphere. We find quantum numbers in agreement with those of the gauge
invariant operators in the N=2 superconformal Chern-Simons theory recently
proposed to be the dual of this M-theory background. This theory is obtained
from the U(N)xU(N) theory through deforming the superpotential by a term
quadratic in one of the superfields. To construct this model explicitly, one
needs to employ monopole operators whose complete understanding is still
lacking. However, for the U(2)xU(2) gauge theory we make a proposal for the
form of the monopole operators which has a number of desired properties. In
particular, this proposal implies enhanced symmetry of the U(2)xU(2) ABJM
theory for k=1,2; it makes its similarity to and subtle difference from the BLG
theory quite explicit.Comment: 32 pages, v2: references added, minor changes, v3: some
clarifications, published versio
Constraining Maximally Supersymmetric Membrane Actions
We study the recent construction of maximally supersymmetric field theory
Lagrangians in three spacetime dimensions that are based on algebras with a
triple product. Assuming that the algebra has a positive definite metric
compatible with the triple product, we prove that the only non-trivial examples
are either the well known case based on a four dimensional algebra or direct
sums thereof.Comment: 11 pages, very minor changes. Reference added. Version to be
published in JHE
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