900 research outputs found

### Hidden 12-dimensional structures in AdS(5)xS(5) and M(4)xR(6) Supergravities

It is shown that AdS(5)xS(5) supergravity has hitherto unnoticed
supersymmetric properties that are related to a hidden 12-dimensional
structure. The totality of the AdS(5)xS(5) supergravity Kaluza-Klein towers is
given by a single superfield that describes the quantum states of a
12-dimensional supersymmetric particle. The particle has super phase space
(X,P,Theta) with (10,2) signature and 32 fermions. The worldline action is
constructed as a generalization of the supersymmetric particle action in
Two-Time Physics. SU(2,2|4) is a linearly realized global supersymmetry of the
2T action. The action is invariant under the gauge symmetries Sp(2,R),
SO(4,2),SO(6), and fermionic kappa. These gauge symmetries insure unitarity and
causality while allowing the reduction of the 12-dimensional super phase space
to the correct super phase space for AdS(5)xS(5) or M(4)xR(6) with 16 fermions
and one time, or other dually related one time spaces. One of the predictions
of this formulation is that all of the SU(2,2|4) representations that describe
Kaluza-Klein towers in AdS(5)xS(5) or M(4)xR(6) supergravity universally have
vanishing eigenvalues for all the Casimir operators. This prediction has been
verified directly in AdS(5)xS(5) supergravity. This suggests that the
supergravity spectrum supports a hidden (10,2) structure. A possible duality
between AdS(5)xS(5) and M(4)xR(6) supergravities is also indicated.
Generalizations of the approach applicable 10-dimensional super Yang Mills
theory and 11-dimensional M-theory are briefly discussed.Comment: LaTeX, 32 pages. v2 includes additional generalizations in the
discussion section. The norm of J has been modified in eqs.(2.6, 3.3, 3.8).
v3 includes a correction to Eq.(5.3

### Interacting Two-Time Physics Field Theory With a BRST Gauge Invariant Action

We construct a field theoretic version of 2T-physics including interactions
in an action formalism. The approach is a BRST formulation based on the
underlying Sp(2,R)gauge symmetry, and shares some similarities with the
approach used to construct string field theory. In our first case of spinless
particles, the interaction is uniquely determined by the BRST gauge symmetry,
and it is different than the Chern-Simons type theory used in open string field
theory. After constructing a BRST gauge invariant action for 2T-physics field
theory with interactions in d+2 dimensions, we study its relation to standard
1T-physics field theory in (d-1)+1 dimensions by choosing gauges. In one gauge
we show that we obtain the Klein-Gordon field theory in (d-1)+1 dimensions with
unique SO(d,2) conformal invariant self interactions at the classical field
level. This SO(d,2) is the natural linear Lorentz symmetry of the 2T field
theory in d+2 dimensions. As indicated in Fig.1, in other gauges we expect to
derive a variety of SO(d,2)invariant 1T-physics field theories as gauge fixed
forms of the same 2T field theory, thus obtaining a unification of 1T-dynamics
in a field theoretic setting, including interactions. The BRST gauge
transformation should play the role of duality transformations among the
1T-physics holographic images of the same parent 2T field theory. The
availability of a field theory action opens the way for studying 2T-physics
with interactions at the quantum level through the path integral approach.Comment: 22 pages, 1 figure, v3 includes corrections of typos and some
comment

### 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 $P_{2n},P_{1m}$ 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

### Dualities among 1T-Field Theories with Spin, Emerging from a Unifying 2T-Field Theory

The relation between two time physics (2T-physics) and the ordinary one time
formulation of physics (1T-physics) is similar to the relation between a
3-dimensional object moving in a room and its multiple shadows moving on walls
when projected from different perspectives. The multiple shadows as seen by
observers stuck on the wall are analogous to the effects of the 2T-universe as
experienced in ordinary 1T spacetime. In this paper we develop some of the
quantitative aspects of this 2T to 1T relationship in the context of field
theory. We discuss 2T field theory in d+2 dimensions and its shadows in the
form of 1T field theories when the theory contains Klein-Gordon, Dirac and
Yang-Mills fields, such as the Standard Model of particles and forces. We show
that the shadow 1T field theories must have hidden relations among themselves.
These relations take the form of dualities and hidden spacetime symmetries. A
subset of the shadows are 1T field theories in different gravitational
backgrounds (different space-times) such as the flat Minkowski spacetime, the
Robertson-Walker expanding universe, AdS(d-k) x S(k) and others, including
singular ones. We explicitly construct the duality transformations among this
conformally flat subset, and build the generators of their hidden SO(d,2)
symmetry. The existence of such hidden relations among 1T field theories, which
can be tested by both theory and experiment in 1T-physics, is part of the
evidence for the underlying d+2 dimensional spacetime and the unifying
2T-physics structure.Comment: 33 pages, LaTe

### 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

### Gravity in 2T-Physics

The field theoretic action for gravitational interactions in d+2 dimensions
is constructed in the formalism of 2T-physics. General Relativity in d
dimensions emerges as a shadow of this theory with one less time and one less
space dimensions. The gravitational constant turns out to be a shadow of a
dilaton field in d+2 dimensions that appears as a constant to observers stuck
in d dimensions. If elementary scalar fields play a role in the fundamental
theory (such as Higgs fields in the Standard Model coupled to gravity), then
their shadows in d dimensions must necessarily be conformal scalars. This has
the physical consequence that the gravitational constant changes at each phase
transition (inflation, grand unification, electro-weak, etc.), implying
interesting new scenarios in cosmological applications. The fundamental action
for pure gravity, which includes the spacetime metric, the dilaton and an
additional auxiliary scalar field all in d+2 dimensions with two times, has a
mix of gauge symmetries to produce appropriate constraints that remove all
ghosts or redundant degrees of freedom. The action produces on-shell classical
field equations of motion in d+2 dimensions, with enough constraints for the
theory to be in agreement with classical General Relativity in d dimensions.
Therefore this action describes the correct classical gravitational physics
directly in d+2 dimensions. Taken together with previous similar work on the
Standard Model of particles and forces, the present paper shows that 2T-physics
is a general consistent framework for a physical theory.Comment: 24 pages, revision includes minor corrections and additional
clarifying materia

### Hidden Symmetries, AdS_D x S^n, and the lifting of one-time-physics to two-time-physics

The massive non-relativistic free particle in d-1 space dimensions has an
action with a surprizing non-linearly realized SO(d,2) symmetry. This is the
simplest example of a host of diverse one-time-physics systems with hidden
SO(d,2) symmetric actions. By the addition of gauge degrees of freedom, they
can all be lifted to the same SO(d,2) covariant unified theory that includes an
extra spacelike and an extra timelike dimension. The resulting action in d+2
dimensions has manifest SO(d,2) Lorentz symmetry and a gauge symmetry Sp(2,R)
and it defines two-time-physics. Conversely, the two-time action can be gauge
fixed to diverse one-time physical systems. In this paper three new gauge fixed
forms that correspond to the non-relativistic particle, the massive
relativistic particle, and the particle in AdS_(d-n) x S^n spacetime will be
discussed. The last case is discussed at the first quantized and field theory
levels as well. For the last case the popularly known symmetry is SO(d-n-1,2) x
SO(n+1), but yet we show that it is symmetric under the larger SO(d,2). In the
field theory version the action is symmetric under the full SO(d,2) provided it
is improved with a quantized mass term that arises as an anomaly from operator
ordering ambiguities. The anomalous cosmological term vanishes for AdS_2 x S^0
and AdS_n x S^n (i.e. d=2n). The strikingly larger symmetry could be
significant in the context of the proposed AdS/CFT duality.Comment: Latex, 23 pages. The term "cosmological constant" that appeared in
the original version has been changed to "mass term". My apologies for the
confusio

### 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

### 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

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