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

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

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

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