918 research outputs found
Superstrings with new supersymmetry in (9,2) and (10,2) dimensions
We construct superstring theories that obey the new supersymmetry algebra
{Q_a , Q_b}=\gamma_{ab}^{mn} P_{1m} P_{2n}, in a Green-Schwarz formalism, with
kappa supersymmetry also of the new type. The superstring is in a system with a
superparticle so that their total momenta are respectively. The
system is covariant and critical in (10,2) dimensions if the particle is
massless and in (9,2) dimensions if the particle is massive. Both the
superstring and superparticle have coordinates with two timelike dimensions but
each behaves effectively as if they have a single timelike dimension. This is
due to gauge symmetries and associated constraints. We show how to generalize
the gauge principle to more intricate systems containing two parts, 1 and 2.
Each part contains interacting constituents, such as p-branes, and each part
behaves effectively as if they have one timelike coordinate, although the full
system has two timelike coordinates. The examples of two superparticles, and of
a superparticle and a superstring, discussed in more detail are a special cases
of such a generalized interacting system.Comment: LaTeX, revtex, 9 page
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
High Spin Gauge Fields and Two-Time Physics
All possible interactions of a point particle with background
electromagnetic, gravitational and higher-spin fields is considered in the
two-time physics worldline formalism in (d,2) dimensions. This system has a
counterpart in a recent formulation of two-time physics in non-commutative
field theory with local Sp(2) symmetry. In either the worldline or field theory
formulation, a general Sp(2) algebraic constraint governs the interactions, and
determines equations that the background fields of any spin must obey. The
constraints are solved in the classical worldline formalism (h-bar=0 limit) as
well as in the field theory formalism (all powers of h-bar). The solution in
both cases coincide for a certain 2T to 1T holographic image which describes a
relativistic particle interacting with background fields of any spin in (d-1,1)
dimensions. Two disconnected branches of solutions exist, which seem to have a
correspondence as massless states in string theory, one containing low spins in
the zero Regge slope limit, and the other containing high spins in the infinite
Regge slope limit.Comment: LaTeX 22 pages. Typos corrected in version
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
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
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