821 research outputs found
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
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
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
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
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
Conformally Exact Metric and Dilaton in String Theory on Curved Spacetime
Using a Hamiltonian approach to gauged WZW models, we present a general
method for computing the conformally exact metric and dilaton, to all orders in
the expansion, for any bosonic, heterotic, or type-II superstring model
based on a coset . We prove the following relations: (i) For type-II
superstrings the conformally exact metric and dilaton are identical to those of
the non-supersymmetric {\it semi-classical} bosonic model except for an overall
renormalization of the metric obtained by . (ii) The exact
expressions for the heterotic superstring are derived from their exact bosonic
string counterparts by shifting the central extension (but an
overall factor remains unshifted). (iii) The combination
is independent of and therefore can be computed in lowest
order perturbation theory as required by the correct formulation of a
conformally invariant path integral measure. The general formalism is applied
to the coset models that are relevant for
string theory on curved spacetime. Explicit expressions for the conformally
exact metric and dilaton for the cases are given. In the
semiclassical limit our results agree with those obtained with
the Lagrangian method up to 1-loop in perturbation theory.Comment: USC-92/HEP-B2, 19 pages and 3 figure
Exact Effective Action and Spacetime Geometry in Gauged WZW Models
We present an effective quantum action for the gauged WZW model
. It is conjectured that it is valid to all orders of the
central extension on the basis that it reproduces the exact spacetime
geometry of the zero modes that was previously derived in the algebraic
Hamiltonian formalism. Besides the metric and dilaton, the new results that
follow from this approach include the exact axion field and the solution of the
geodesics in the exact geometry. It is found that the axion field is generally
non-zero at higher orders of even if it vanishes at large . We work
out the details in two specific coset models, one non-abelian, i.e.
and one abelian, i.e SL(2,\IR)\otimes
SO(1,1)^{d-2}/SO(1,1). The simplest case SL(2,\IR)/\IR corresponds to a
limit.Comment: 20 pages, harvmac, USC-93/HEP-B1, (The exact general expression for
the dilaton is added in Sec.5
Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions
We propose an approximation to the ground state of Yang-Mills theory,
quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills
Schrodinger equation in both the free-field limit, and in a strong-field zero
mode limit. Our proposal contains a single parameter with dimensions of mass;
confinement via dimensional reduction is obtained if this parameter is
non-zero, and a non-zero value appears to be energetically preferred. A method
for numerical simulation of this vacuum state is developed. It is shown that if
the mass parameter is fixed from the known string tension in 2+1 dimensions,
the resulting mass gap deduced from the vacuum state agrees, to within a few
percent, with known results for the mass gap obtained by standard lattice Monte
Carlo methods.Comment: 14 pages, 9 figures. v2: Typos corrected. v3: added a new section
discussing alternative (new variables) approaches, and fixed a problem with
the appearance of figures in the pdf version. Version to appear in Phys Rev
Progress on testing Lorentz symmetry with MICROSCOPE
The Weak Equivalence Principle (WEP) and the local Lorentz invariance (LLI)
are two major assumptions of General Relativity (GR). The MICROSCOPE mission,
currently operating, will perform a test of the WEP with a precision of
. The data will also be analysed at SYRTE for the purposes of a LLI
test realised in collaboration with J. Tasson (Carleton College, Minnesota) and
Q. Bailey (Embry-Riddle Aeronautical University, Arizona). This study will be
performed in a general framework, called the Standard Model Extension (SME),
describing Lorentz violations that could appear at Planck scale (
GeV). The SME allows us to derive a Lorentz violating observable designed for
the MICROSCOPE experiment and to search for possible deviations from LLI in the
differential acceleration of the test masses
Global Analysis of New Gravitational Singularities in String and Particle Theories
We present a global analysis of the geometries that arise in non-compact
current algebra (or gauged WZW) coset models of strings and particles
propagating in curved space-time. The simplest case is the 2d black hole. In
higher dimensions these geometries describe new and much more complex
singularities. For string and particle theories (defined in the text) we
introduce general methods for identifying global coordinates and give the
general exact solution for the geodesics for any gauged WZW model for any
number of dimensions. We then specialize to the 3d geometries associated with
(and also ) and discuss in detail the global
space, geodesics, curvature singularities and duality properties of this space.
The large-small (or mirror) type duality property is reformulated as an
inversion in group parameter space. The 3d global space has two topologically
distinct sectors, with patches of different sectors related by duality. The
first sector has a singularity surface with the topology of ``pinched double
trousers". It can be pictured as the world sheet of two closed strings that
join into a single closed string and then split into two closed strings, but
with a pinch in each leg of the trousers. The second sector has a singularity
surface with the topology of ``double saddle", pictured as the world sheets of
two infinite open strings that come close but do not touch. We discuss the
geodesicaly complete spaces on each side of these surfaces and interpret the
motion of particles in physical terms. A cosmological interpretation is
suggested and comments are mode on possible physical applications.Comment: 31 pages, plus 4 figure
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