991 research outputs found
A Hidden Twelve-Dimensional SuperPoincare Symmetry In Eleven Dimensions
First, we review a result in our previous paper, of how a ten-dimensional
superparticle, taken off-shell, has a hidden eleven-dimensional superPoincare
symmetry. Then, we show that the physical sector is defined by three
first-class constraints which preserve the full eleven-dimensional symmetry.
Applying the same concepts to the eleven dimensional superparticle, taken
off-shell, we discover a hidden twelve dimensional superPoincare symmetry that
governs the theory.Comment: 13 page
Two-Time Physics with gravitational and gauge field backgrounds
It is shown that all possible gravitational, gauge and other interactions
experienced by particles in ordinary d-dimensions (one-time) can be described
in the language of two-time physics in a spacetime with d+2 dimensions. This is
obtained by generalizing the worldline formulation of two-time physics by
including background fields. A given two-time model, with a fixed set of
background fields, can be gauged fixed from d+2 dimensions to (d-1) +1
dimensions to produce diverse one-time dynamical models, all of which are
dually related to each other under the underlying gauge symmetry of the unified
two-time theory. To satisfy the gauge symmetry of the two-time theory the
background fields must obey certain coupled differential equations that are
generally covariant and gauge invariant in the target d+2 dimensional
spacetime. The gravitational background obeys a null homothety condition while
the gauge field obeys a differential equation that generalizes a similar
equation derived by Dirac in 1936. Explicit solutions to these coupled
equations show that the usual gravitational, gauge, and other interactions in d
dimensions may be viewed as embedded in the higher d+2 dimensional space, thus
displaying higher spacetime symmetries that otherwise remain hidden.Comment: Latex, 19 pages, references adde
Gauge symmetry in phase space with spin, a basis for conformal symmetry and duality among many interactions
We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space
(X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime
with two times X^0,, X^0', unifies many physical systems which ordinarily are
described by a 1-time formulation. Different systems of 1-time physics emerge
by choosing gauges that embed ordinary time in d+2 dimensions in different
ways. The embeddings have different topology and geometry for the choice of
time among the d+2 dimensions. Thus, 2-time physics unifies an infinite number
of 1-time physical interacting systems, and establishes a kind of duality among
them. One manifestation of the two times is that all of these physical systems
have the same quantum Hilbert space in the form of a unique representation of
SO(d,2) with the same Casimir eigenvalues. By changing the number n of spinning
degrees of freedom the gauge group changes to OSp(n/2). Then the eigenvalue of
the Casimirs of SO(d,2) depend on n and then the content of the 1-time physical
systems that are unified in the same representation depend on n. The models we
study raise new questions about the nature of spacetime.Comment: Latex, 42 pages. v2 improvements in AdS section. In v3 sec.6.2 is
modified; the more general potential is limited to a smaller clas
Noncommutative Sp(2,R) Gauge Theories - A Field Theory Approach to Two-Time Physics
Phase-space and its relativistic extension is a natural space for realizing
Sp(2,R) symmetry through canonical transformations. On a Dx2 dimensional
covariant phase-space, we formulate noncommutative field theories, where
Sp(2,R) plays a role as either a global or a gauge symmetry group. In both
cases these field theories have potential applications, including certain
aspects of string theories, M-theory, as well as quantum field theories. If
interpreted as living in lower dimensions, these theories realize Poincare'
symmetry linearly in a way consistent with causality and unitarity. In case
Sp(2,R) is a gauge symmetry, we show that the spacetime signature is determined
dynamically as (D-2,2). The resulting noncommutative Sp(2,R) gauge theory is
proposed as a field theoretical formulation of two-time physics: classical
field dynamics contains all known results of `two-time physics', including the
reduction of physical spacetime from D to (D-2) dimensions, with the associated
`holography' and `duality' properties. In particular, we show that the solution
space of classical noncommutative field equations put all massless scalar,
gauge, gravitational, and higher-spin fields in (D-2) dimensions on
equal-footing, reminiscent of string excitations at zero and infinite tension
limits.Comment: 32 pages, LaTe
Conformal Symmetry and Duality between Free Particle, H-atom and Harmonic Oscillator
We establish a duality between the free massless relativistic particle in d
dimensions, the non-relativistic hydrogen atom (1/r potential) in (d-1) space
dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass
given as the lightcone momentum of an additional dimension. The duality is in
the sense that the classical action of these systems are gauge fixed forms of
the same worldline gauge theory action at the classical level, and they are all
described by the same unitary representation of the conformal group SO(d,2) at
the quantum level. The worldline action has a gauge symmetry Sp(2) which treats
canonical variables (x,p) as doublets and exists only with a target spacetime
that has d spacelike dimensions and two timelike dimensions. This spacetime is
constrained due to the gauge symmetry, and the various dual solutions
correspond to solutions of the constraints with different topologies. For
example, for the H-atom the two timelike dimensions X^{0'},X^{0} live on a
circle. The model provides an example of how realistic physics can be viewed as
existing in a larger covariant space that includes two timelike coordinates,
and how the covariance in the larger space unifies different looking physics
into a single system.Comment: Latex, 23 pages, minor improvements. In v3 a better gauge choice for
u for the H-atom is made; the results are the sam
Supersymmetric Two-Time Physics
We construct an Sp(2,R) gauge invariant particle action which possesses
manifest space-time SO(d,2) symmetry, global supersymmetry and kappa
supersymmetry. The global and local supersymmetries are non-abelian
generalizations of Poincare type supersymmetries and are consistent with the
presence of two timelike dimensions. In particular, this action provides a
unified and explicit superparticle representation of the superconformal groups
OSp(N/4), SU(2,2/N) and OSp(8*/N) which underlie various AdS/CFT dualities in
M/string theory. By making diverse Sp(2,R) gauge choices our action reduces to
diverse one-time physics systems, one of which is the ordinary (one-time)
massless superparticle with superconformal symmetry that we discuss explicitly.
We show how to generalize our approach to the case of superalgebras, such as
OSp(1/32), which do not have direct space-time interpretations in terms of only
zero branes, but may be realizable in the presence of p-branes.Comment: Latex, 18 page
Non standard parametrizations and adjoint invariants of classical groups
We obtain local parametrizations of classical non-compact Lie groups where
adjoint invariants under maximal compact subgroups are manifest. Extension to
non compact subgroups is straightforward. As a by-product parametrizations of
the same type are obtained for compact groups. They are of physical interest in
any theory gauge invariant under the adjoint action, typical examples being the
two dimensional gauged Wess-Zumino-Witten-Novikov models where these
coordinatizations become of extreme usefulness to get the background fields
representing the vacuum expectation values of the massless modes of the
associated (super) string theory.Comment: 11 pages, latex file, La Plata preprint Th-99/01. Minor changes in
the introduction, version to appear in Physics Letters
S-Theory
The representation theory of the maximally extended superalgebra with 32
fermionic and 528 bosonic generators is developed in order to investigate
non-perturbative properties of the democratic secret theory behind strings and
other p-branes. The presence of Lorentz non-singlet central extensions is
emphasized, their role for understanding up to 13 hidden dimensions and their
physical interpretation as boundaries of p-branes is elucidated. The criteria
for a new larger set of BPS-like non-perturbative states is given and the
methods of investigation are illustrated with several explicit examples.Comment: Latex, 18 papge
Free Fields Equations For Space-Time Algebras With Tensorial Momentum
Free field equations, with various spins, for space-time algebras with
second-rank tensor (instead of usual vector) momentum are constructed. Similar
algebras are appearing in superstring/M theories. The most attention is payed
to the gauge invariance properties, particularly the spin two equations with
gauge invariance are constructed for dimensions 2+2 and 2+4 and connection to
Einstein equation and diffeomorphism invariance is established
Superstar in Noncommutative Superspace via Covariant Quantization of the Superparticle
A covariant quantization method is developed for the off-shell superparticle
in 10 dimensions. On-shell it is consistent with lightcone quantization, while
off-shell it gives a noncommutative superspace that realizes non-linearly a
hidden 11-dimensional super Poincare symmetry. The non-linear commutation rules
are then used to construct the supersymmetric generalization of the covariant
Moyal star product in noncommutative superspace. As one of the possible
applications, we propose this new product as the star product in supersymmetric
string field theory. Furthermore, the formalism introduces new techniques and
concepts in noncommutative (super)geometry.Comment: 17 pages, LaTe
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