770 research outputs found
Postmodern String Theory: Stochastic Formulation
In this paper we study the dynamics of a statistical ensemble of strings,
building on a recently proposed gauge theory of the string geodesic field. We
show that this stochastic approach is equivalent to the Carath\'eodory
formulation of the Nambu-Goto action, supplemented by an averaging procedure
over the family of classical string world-sheets which are solutions of the
equation of motion. In this new framework, the string geodesic field is
reinterpreted as the Gibbs current density associated with the string
statistical ensemble. Next, we show that the classical field equations derived
from the string gauge action, can be obtained as the semi-classical limit of
the string functional wave equation. For closed strings, the wave equation
itself is completely analogous to the Wheeler-DeWitt equation used in quantum
cosmology. Thus, in the string case, the wave function has support on the space
of all possible spatial loop configurations. Finally, we show that the string
distribution induces a multi-phase, or {\it cellular} structure on the
spacetime manifold characterized by domains with a purely Riemannian geometry
separated by domain walls over which there exists a predominantly Weyl
geometry.Comment: 24pages, ReVTe
Langevin Analysis of Eternal Inflation
It has been widely claimed that inflation is generically eternal to the
future, even in models where the inflaton potential monotonically increases
away from its minimum. The idea is that quantum fluctuations allow the field to
jump uphill, thereby continually revitalizing the inflationary process in some
regions. In this paper we investigate a simple model of this process,
pertaining to inflation with a quartic potential, in which analytic progress
may be made. We calculate several quantities of interest, such as the expected
number of inflationary efolds, first without and then with various selection
effects. With no additional weighting, the stochastic noise has little impact
on the total number of inflationary efoldings even if the inflaton starts with
a Planckian energy density. A "rolling" volume factor, i.e. weighting in
proportion to the volume at that time, also leads to a monotonically decreasing
Hubble constant and hence no eternal inflation. We show how stronger selection
effects including a constraint on the initial and final states and weighting
with the final volume factor can lead to a picture similar to that usually
associated with eternal inflation.Comment: 22 pages, 2 figure
Nambu-Goldstone Mechanism in Real-Time Thermal Field Theory
In a one-generation fermion condensate scheme of electroweak symmetry
breaking, it is proven based on Schwinger-Dyson equation in the real-time
thermal field theory in the fermion bubble diagram approximation that, at
finite temperature below the symmetry restoration temperature , a
massive Higgs boson and three massless Nambu-Goldstone bosons could emerge from
the spontaneous breaking of electroweak group
if the two fermion flavors in the one generation are mass-degenerate, thus
Goldstone Theorem is rigorously valid in this case. However, if the two fermion
flavors have unequal masses, owing to "thermal flactuation", the Goldstone
Theorem will be true only approximately for a very large momentum cut-off
in zero temperature fermion loop or for low energy scales. All
possible pinch singularities are proven to cancel each other, as is expected in
a real-time thermal field theory.Comment: 11 pages, revtex, no figure, Phys. Rev. D, to appea
Spinors for Spinning p-Branes
The group of the p-brane world volume preserving diffeomorphism is
considered. The infinite-dimensional spinors of this group are related, by the
nonlinear realization techniques, to the corresponding spinors of its linear
subgroup, that are constructed explicitly. An algebraic construction of the
Virasoro and Neveu-Schwarz-Ramond algebras, based on this infinite-dimensional
spinors and tensors, is demonstrated.Comment: 18 page
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
Renormalization Group Approach to Cosmological Back Reaction Problems
We investigated the back reaction of cosmological perturbations on the
evolution of the universe using the second order perturbation of the Einstein's
equation. To incorporate the back reaction effect due to the inhomogeneity into
the framework of the cosmological perturbation, we used the renormalization
group method. The second order zero mode solution which appears by the
non-linearities of the Einstein's equation is regarded as a secular term of the
perturbative expansion, we renormalized a constant of integration contained in
the background solution and absorbed the secular term to this constant. For a
dust dominated universe, using the second order gauge invariant quantity, we
derived the renormalization group equation which determines the effective
dynamics of the Friedman-Robertson-Walker universe with the back reaction
effect in a gauge invariant manner. We obtained the solution of the
renormalization group equation and found that perturbations of the scalar mode
and the long wavelength tensor mode works as positive spatial curvature, and
the short wavelength tensor mode as radiation fluid.Comment: 18 pages, revtex, to appear in Phys. Rev.
QCD and String Theory
This talk begins with some history and basic facts about string theory and
its connections with strong interactions. Comparisons of stacks of Dirichlet
branes with curved backgrounds produced by them are used to motivate the
AdS/CFT correspondence between superconformal gauge theory and string theory on
a product of Anti-de Sitter space and a compact manifold. The ensuing duality
between semi-classical spinning strings and long gauge theory operators is
briefly reviewed. Strongly coupled thermal SYM theory is explored via a black
hole in 5-dimensional AdS space, which leads to explicit results for its
entropy and shear viscosity. A conjectured universal lower bound on the
viscosity to entropy density ratio, and its possible relation to recent results
from RHIC, are discussed. Finally, some available results on string duals of
confining gauge theories are briefly reviewed.Comment: 12 pages, prepared for the Proceedings of the 2005 Lepton-Photon
Symposium; v2: minor revisions, references added, the version to appear in
the proceeding
Effective action of a 2+1 dimensional system of nonrelativistic fermions in the presence of a uniform magnetic field: dissipation effects
The effective action of nonrelativistic fermions in 2+1 dimensions is
analyzed at finite temperature and chemical potential in the presence of a
uniform magnetic field perpendicular to the plane. The method used is a
generalization of the derivative expansion technique. The induced Chern-Simons
term is computed and shown to exhibit the Hall quantization. Effects of
dissipation due to collisions are also analyzed.Comment: 12 page
No First-Order Phase Transition in the Gross-Neveu Model?
Within a variational calculation we investigate the role of baryons for the
structure of dense matter in the Gross-Neveu model. We construct a trial ground
state at finite baryon density which breaks translational invariance. Its
scalar potential interpolates between widely spaced kinks and antikinks at low
density and the value zero at infinite density. Its energy is lower than the
one of the standard Fermi gas at all densities considered. This suggests that
the discrete gamma_5 symmetry of the Gross-Neveu model does not get restored in
a first order phase transition at finite density, at variance with common
wisdom.Comment: 16 pages, 7 figures, LaTe
Dynamical Symmetry Breaking in Models with the Yukawa Interaction
We discuss models with a massless fermion and a self-interacting massive
scalar field with the Yukawa interaction. The chiral condensate and the fermion
mass are calculated analytically. It is shown that the models have a phase
transition as a function of the squared mass of the scalar field.Comment: 7 pages, no figures, in Eqs. (7) and (11) one coefficient was change
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