2,968 research outputs found
Background Independent Algebraic Structures in Closed String Field Theory
We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann
surfaces. This algebra is background independent in that it makes no reference
to a state space of a conformal field theory. Conformal theories define a
homomorphism of this algebra to the BV algebra of string functionals. The
construction begins with a graded-commutative free associative algebra \C
built from the vector space whose elements are orientable subspaces of moduli
spaces of punctured Riemann surfaces. The typical element here is a surface
with several connected components. The operation of sewing two
punctures with a full twist is shown to be an odd, second order derivation that
squares to zero. It follows that (\C, \Delta) is a Batalin-Vilkovisky
algebra. We introduce the odd operator , where
is the boundary operator. It is seen that , and that
consistent closed string vertices define a cohomology class of . This
cohomology class is used to construct a Lie algebra on a quotient space of
\C. This Lie algebra gives a manifestly background independent description of
a subalgebra of the closed string gauge algebra.Comment: phyzzx.tex, MIT-CTP-234
Rolling Tachyon Solution in Vacuum String Field Theory
We construct a time-dependent solution in vacuum string field theory and
investigate whether the solution can be regarded as a rolling tachyon solution.
First, compactifying one space direction on a circle of radius R, we construct
a space-dependent solution given as an infinite number of *-products of a
string field with center-of-mass momentum dependence of the form e^{-b p^2/4}.
Our time-dependent solution is obtained by an inverse Wick rotation of the
compactified space direction. We focus on one particular component field of the
solution, which takes the form of the partition function of a Coulomb system on
a circle with temperature R^2. Analyzing this component field both analytically
and numerically using Monte Carlo simulation, we find that the parameter b in
the solution must be set equal to zero for the solution to approach a finite
value in the large time limit x^0\to\infty. We also explore the possibility
that the self-dual radius R=\sqrt{\alpha'} is a phase transition point of our
Coulomb system.Comment: 39 pages, 17 figures, v3: references adde
Boundary states as exact solutions of (vacuum) closed string field theory
We show that the boundary states are idempotent B*B=B with respect to the
star product of HIKKO type closed string field theory. Variations around the
boundary state correctly reproduce the open string spectrum with the gauge
symmetry. We explicitly demonstrate it for the tachyonic and massless vector
modes. The idempotency relation may be regarded as the equation of motion of
closed string field theory at a possible vacuum.Comment: 30 pages, 2 figures, v3:regularization improve
Time Dependent Solution in Cubic String Field Theory
We study time dependent solutions in cubic open string field theory which are
expected to describe the configuration of the rolling tachyon. We consider the
truncated system consisting of component fields of level zero and two, which
are expanded in terms of cosh n x^0 modes. For studying the large time behavior
of the solution we need to know the coefficients of all and, in particular,
large n modes. We examine numerically the coefficients of the n-th mode, and
find that it has the leading n-dependence of the form (-\beta)^n \lambda^{-n^2}
multiplied by a peculiar subleading part with peaks at
n=2^m=4,8,16,32,64,128,.... This behavior is also reproduced analytically by
solving simplified equations of motion of the tachyon system.Comment: 22 pages, 12 figures, LaTeX2e, v3:minor correction
Patterns in Open String Field Theory Solutions
In open string field theory the kinetic operator mixes matter and ghost
sectors, and thus the ghost structure of classical solutions is not universal.
Nevertheless, we have found from numerical analysis that certain ratios of
expectation values for states involving pure ghost excitations appear to be
universal. We give an analytic expression for these ratios and find good
evidence that they are common to all known solutions of open string field
theory, including the tachyon vacuum solution, lump solutions and string fields
representing marginal deformations. We also draw attention to a close
correspondence between the expectation values for the pure matter components in
the tachyon vacuum solution and those in the solution of a simpler equation for
a ghost number zero string field. Finally we observe that the action of L_0 on
the tachyon condensate gives a state that is approximately factorized into a
matter and a ghost part.Comment: 21 pages, LaTe
Vacuum Values for Auxiliary String Fields
Auxiliary string fields are introduced in light-cone gauge string field
theory in order to express contact interactions as contractions of cubic
vertices. The auxiliary field in the purely closed-string bosonic theory may be
given a non-zero expectation value, leading to a phase in which world-sheets
have boundaries.Comment: 13 pages, DAMTP/94-2
An Analytical Construction of the SRB Measures for Baker-type Maps
For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle
and Bowen showed the existence of an invariant measure (SRB measure) weakly
attracting the temporal average of any initial distribution that is absolutely
continuous with respect to the Lebesgue measure. Recently, the SRB measures
were found to be related to the nonequilibrium stationary state distribution
functions for thermostated or open systems. Inspite of the importance of these
SRB measures, it is difficult to handle them analytically because they are
often singular functions. In this article, for three kinds of Baker-type maps,
the SRB measures are analytically constructed with the aid of a functional
equation, which was proposed by de Rham in order to deal with a class of
singular functions. We first briefly review the properties of singular
functions including those of de Rham. Then, the Baker-type maps are described,
one of which is non-conservative but time reversible, the second has a
Cantor-like invariant set, and the third is a model of a simple chemical
reaction . For the second example, the
cases with and without escape are considered. For the last example, we consider
the reaction processes in a closed system and in an open system under a flux
boundary condition. In all cases, we show that the evolution equation of the
distribution functions partially integrated over the unstable direction is very
similar to de Rham's functional equation and, employing this analogy, we
explicitly construct the SRB measures.Comment: 53 pages, 10 figures, to appear in CHAO
Probability of a Solution to the Solar Neutrino Problem Within the Minimal Standard Model
Tests, independent of any solar model, can be made of whether solar neutrino
experiments are consistent with the minimal Standard Model (stable, massless
neutrinos). If the experimental uncertainties are correctly estimated and the
sun is generating energy by light-element fusion in quasi-static equilibrium,
the probability of a standard-physics solution is less than 2%. Even when the
luminosity constraint is abandoned, the probability is not more than 4%. The
sensitivity of the conclusions to input parameters is explored.Comment: PRL, Revtex, 1 figure, 5 page
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