135 research outputs found
Space-Time Noncommutativity, Discreteness of Time and Unitarity
Violation of unitarity for noncommutative field theory on compact space-times
is considered. Although such theories are free of ultraviolet divergences, they
still violate unitarity while in a usual field theory such a violation occurs
when the theory is nonrenormalizable. The compactness of space-like coordinates
implies discreteness of the time variable which leads to appearance of
unphysical modes and violation of unitarity even in the absence of a
star-product in the interaction terms. Thus, this conclusion holds also for
other quantum field theories with discrete time. Violation of causality, among
others, occurs also as the nonvanishing of the commutation relations between
observables at space-like distances with a typical scale of noncommutativity.
While this feature allows for a possible violation of the spin-statistics
theorem, such a violation does not rescue the situation but makes the scale of
causality violation as the inverse of the mass appearing in the considered
model, i.e., even more severe. We also stress the role of smearing over the
noncommutative coordinates entering the field operator symbols.Comment: 10 pages, plain LaTe
Astrophysical Implications of the Superstring-Inspired E_6 Unification and Shadow Theta-Particles
We have developed a concept of parallel existence of the ordinary (O) and
mirror (M), or shadow (Sh) worlds. E_6 unification, inspired by superstring
theory, restores the broken mirror parity at the scale ~ 10^18 GeV. With the
aim to explain the tiny cosmological constant, we consider the breakings: E_6
-> SO(10) X U(1)_Z - in the O-world, and E'_6 -> SU(6)' X SU(2)'_\theta - in
the Sh-world. We assume the existence of shadow \theta-particles and the low
energy symmetry group SU(3)'_C X SU(2)'_L X SU(2)'_\theta X U(1)'_Y in the
shadow world, instead of the Standard Model. The additional non-Abelian
SU(2)'_\theta group with massless gauge fields, "thetons", has a macroscopic
confinement radius 1/\Lambda'_\theta. The assumption that
\Lambda'_\theta\approx 2.3 X 10^-3 eV explains the tiny cosmological constant
given by recent astrophysical measurements. Searching for the Dark Matter (DM),
it is possible to observe and study various signals of theta-particles.Comment: 6 pages, 2 figures, presented at "Invisble Universe International
Conference", Palais de l'UNESCO, Paris, France, June 29 - July 3, 200
Quantum Black Holes, Elliptic Genera and Spectral Partition Functions
We study M-theory and D-brane quantum partition functions for microscopic
black hole ensembles within the context of the AdS/CFT correspondence in terms
of highest weight representations of infinite-dimensional Lie algebras,
elliptic genera, and Hilbert schemes, and describe their relations to elliptic
modular forms. The common feature in our examples lie in the modular properties
of the characters of certain representations of the pertinent affine Lie
algebras, and in the role of spectral functions of hyperbolic three-geometry
associated with q-series in the calculation of elliptic genera. We present new
calculations of supergravity elliptic genera on local Calabi-Yau threefolds in
terms of BPS invariants and spectral functions, and also of equivariant D-brane
elliptic genera on generic toric singularities. We use these examples to
conjecture a link between the black hole partition functions and elliptic
cohomology.Comment: 42 page
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