611 research outputs found
Dirac's Footsteps and Supersymmetry
One hundred years after its creator's birth, the Dirac equation stands as the
cornerstone of XXth Century physics. But it is much more, as it carries the
seeds of supersymmetry. Dirac also invented the light-cone, or "front form"
dynamics, which plays a crucial role in string theory and in elucidating the
finiteness of N=4 Yang-Mills theory. The light-cone structure of
eleven-dimensional supergravity (N=8 supergravity in four dimensions) suggests
a group-theoretical interpretation of its divergences. We speculate they could
be compensated by an infinite number of triplets of massless higher spin
fields, each obeying a Dirac-like equation associated with the coset
. The divergences are proportional to the trace over a non-compact
structure containing the compact form of . Its nature is still unknown,
but it could show the way to -theory.Comment: Invited Talk at Dirac's Centennial Symposium, Tallahasse, Florida,
Dec 200
What is the discrete gauge symmetry of the R-parity violating MSSM?
The lack of experimental evidence for supersymmetry motivates R-parity
violating realizations of the MSSM. Dropping R-parity, alternative symmetries
have to be imposed in order to stabilize the proton. We determine the possible
discrete R and non-R symmetries, which allow for renormalizable R-parity
violating terms in the superpotential and which, at the effective level, are
consistent with the constraints from nucleon decay. Assuming a gauge origin, we
require the symmetry to be discrete gauge anomaly-free, allowing also for
cancellation via the Green Schwarz mechanism. Furthermore, we demand lepton
number violating neutrino mass terms either at the renormalizable or
non-renormalizable level. In order to solve the mu problem, the discrete Z_N or
Z_N^R symmetries have to forbid any bilinear superpotential operator at tree
level. In the case of renormalizable baryon number violation the smallest
possible symmetry satisfying all conditions is a unique hexality Z_6^R. In the
case of renormalizable lepton number violation the smallest symmetries are two
hexalities, one Z_6 and one Z_6^R.Comment: 25 pages, version to appear in PR
Torsion and Gravitation: A new view
According to the teleparallel equivalent of general relativity, curvature and
torsion are two equivalent ways of describing the same gravitational field.
Despite equivalent, however, they act differently: whereas curvature yields a
geometric description, in which the concept of gravitational force is absent,
torsion acts as a true gravitational force, quite similar to the Lorentz force
of electrodynamics. As a consequence, the right-hand side of a
spinless-particle equation of motion (which would represent a gravitational
force) is always zero in the geometric description, but not in the teleparallel
case. This means essentially that the gravitational coupling prescription can
be minimal only in the geometric case. Relying on this property, a new
gravitational coupling prescription in the presence of curvature and torsion is
proposed. It is constructed in such a way to preserve the equivalence between
curvature and torsion, and its basic property is to be equivalent with the
usual coupling prescription of general relativity. According to this view, no
new physics is connected with torsion, which appears as a mere alternative to
curvature in the description of gravitation. An application of this formulation
to the equations of motion of both a spinless and a spinning particle is madeComment: To appear on IJMP
Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids
The path integral for randomly forced incompressible fluids is shown to have
an underlying Becchi-Rouet-Stora (BRS) symmetry as a consequence of Galilean
invariance. This symmetry must be respected to have a consistent generating
functional, free from both an overall infinite factor and spurious relations
amongst correlation functions. We present a procedure for respecting this BRS
symmetry, akin to gauge fixing in quantum field theory. Relations are derived
between correlation functions of this gauge fixed, BRS symmetric theory,
analogous to the Slavnov-Taylor identities of quantum field theory.Comment: 5 pages, no figures, In Press Physical Review Letters, 200
Confinement in the 3-dimensional Gross-Neveu model
We consider the -components 3-dimensional massive Gross-Neveu model
compactified in one spatial direction, the system being constrained to a slab
of thickness . We derive a closed formula for the effective renormalized
-dependent coupling constant in the large-N limit, using bag-model boundary
conditions. For values of the fixed coupling constant in absence of boundaries
, we obtain ultra-violet asymptotic
freedom (for ) and confinement for a length such that , being the fermionic mass. Taking
for an average of the masses of the quarks composing the proton, we obtain
a confining legth which is comparable with an estimated proton
diameter.Comment: Latex, 4 pages, 2 figures (one new), some changes in tex
Anti-shielding Effect and Negative Temperature in Instantaneously Reversed Electric Fields and Left-Handed Media
The connections between the anti-shielding effect, negative absolute
temperature and superluminal light propagation in both the instantaneously
reversed electric field and the left-handed media are considered in the present
paper. The instantaneous inversion of the exterior electric field may cause the
electric dipoles into the state of negative absolute temperature and therefore
give rise to a negative effective mass term of electromagnetic field (i. e.,
the electromagnetic field propagating inside the negative-temperature medium
will acquire an imaginary rest mass), which is said to result in the potential
superluminality effect of light propagation in this anti-shielding dielectric.
In left-handed media, such phenomena may also arise.Comment: 9 pages, Late
The U(1)A anomaly in noncommutative SU(N) theories
We work out the one-loop anomaly for noncommutative SU(N) gauge
theories up to second order in the noncommutative parameter .
We set and conclude that there is no breaking of the classical
symmetry of the theory coming from the contributions that are either
linear or quadratic in . Of course, the ordinary anomalous
contributions will be still with us. We also show that the one-loop
conservation of the nonsinglet currents holds at least up to second order in
. We adapt our results to noncommutative gauge theories with
SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde
Eleven-Dimensional Supergravity in Light-Cone Superspace
We show that Supergravity in eleven dimensions can be described in terms of a
constrained superfield on the light-cone, without the use of auxiliary fields.
We build its action to first order in the gravitational coupling constant
\kappa, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for
N=4 Yang-Mills, by extending the transverse derivatives into superspace. The
eleven-dimensional SuperPoincare algebra is constructed and a fourth order
interaction is conjectured.Comment: 18 page
Hodge Dual for Soldered Bundles
In order to account for all possible contractions allowed by the presence of
the solder form, a generalized Hodge dual is defined for the case of soldered
bundles. Although for curvature the generalized dual coincides with the usual
one, for torsion it gives a completely new dual definition. Starting from the
standard form of a gauge lagrangian for the translation group, the generalized
Hodge dual yields precisely the lagrangian of the teleparallel equivalent of
general relativity, and consequently also the Einstein-Hilbert lagrangian of
general relativity.Comment: 8 pages, no figures. Accepted for publication in Journal of Physics
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