15,077 research outputs found
Monotonicity of average return probabilities for random walks in random environments
We extend a result of Lyons (2016) from fractional tiling of finite graphs to
a version for infinite random graphs. The most general result is as follows.
Let be a unimodular probability measure on rooted networks
with positive weights on its edges and with a percolation subgraph of
with positive weights on its edges. Let denote the
conditional law of given . Assume that is a constant -a.s. We show that if
-a.s. whenever is adjacent to , then Comment: 9 pp., 4 figure
Elementary Particles and Spin Representations
We emphasize that the group-theoretical considerations leading to SO(10)
unification of electro-weak and strong matter field components naturally extend
to space-time components, providing a truly unified description of all
generation degrees of freedoms in terms of a single chiral spin representation
of one of the groups SO(13,1), SO(9,5), SO(7,7) or SO(3,11). The realization of
these groups as higher dimensional space-time symmetries produces unification
of all fundamental fermions is a single space-time spinor.Comment: 4 page
On non- solutions to the Seiberg-Witten equations
We show that a previous paper of Freund describing a solution to the
Seiberg-Witten equations has a sign error rendering it a solution to a related
but different set of equations. The non- nature of Freund's solution is
discussed and clarified and we also construct a whole class of solutions to the
Seiberg-Witten equations.Comment: 8 pages, Te
Are There Oscillations in the Baryon/Meson Ratio?
All available data indicate a surplus of baryon states over meson states for
energies greater than about 1.5 GeV. Since hadron-scale string theory suggests
that their numbers should become equal with increasing energy, it has recently
been proposed that there must exist exotic mesons with masses just above 1.7
GeV in order to fill the deficit. We demonstrate that a string-like picture is
actually consistent with the present numbers of baryon and meson states, and in
fact predicts regular oscillations in their ratio. This suggests a different
role for new hadronic states.Comment: 14 pages (RevTeX), McGill/92-0
Nambu-Goldstone Modes in Gravitational Theories with Spontaneous Lorentz Breaking
Spontaneous breaking of Lorentz symmetry has been suggested as a possible
mechanism that might occur in the context of a fundamental Planck-scale theory,
such as string theory or a quantum theory of gravity. However, if Lorentz
symmetry is spontaneously broken, two sets of questions immediately arise: what
is the fate of the Nambu-Goldstone modes, and can a Higgs mechanism occur? A
brief summary of some recent work looking at these questions is presented here.Comment: 6 pages. Presented at the meeting "From Quantum to Cosmos,"
Washington, D.C., May 2006; published in Int. J. Mod. Phys. D16:2357-2363,
200
SUGRA Noether Charges
In this work a generic set of boundary conditions for SUGRA
is proposed. This conditions defines that Hamiltonian charges equals Noether
ones, including supercharge
Quantum critical transport, duality, and M-theory
We consider charge transport properties of 2+1 dimensional conformal field
theories at non-zero temperature. For theories with only Abelian U(1) charges,
we describe the action of particle-vortex duality on the
hydrodynamic-to-collisionless crossover function: this leads to powerful
functional constraints for self-dual theories. For the n=8 supersymmetric,
SU(N) Yang-Mills theory at the conformal fixed point, exact
hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can
be obtained in the large N limit by applying the AdS/CFT correspondence to
M-theory. In the gravity theory, fluctuating currents are mapped to fluctuating
gauge fields in the background of a black hole in 3+1 dimensional anti-de
Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory
implies that the correlators of the R-currents obey a functional constraint
similar to that found from particle-vortex duality in 2+1 dimensional Abelian
theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a
"holographic self duality" in the large N limit, and perhaps more generally.Comment: 35 pages, 4 figures; (v2) New appendix on CFT2, corrected
normalization of gauge field action, added ref
Superevolution
Usually, in supersymmetric theories, it is assumed that the time-evolution of
states is determined by the Hamiltonian, through the Schr\"odinger equation.
Here we explore the superevolution of states in superspace, in which the
supercharges are the principal operators. The superevolution equation is
consistent with the Schr\"odinger equation, but it avoids the usual degeneracy
between bosonic and fermionic states. We discuss superevolution in
supersymmetric quantum mechanics and in a simple supersymmetric field theory.Comment: 23 page
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