2,309 research outputs found
Gauge Structure of Vacuum String Field Theory
We study the gauge structure of vacuum string field theory expanded around
the D-brane solution, namely, the gauge transformation and the transversality
condition of the massless vector fluctuation mode. We find that the gauge
transformation on massless vector field is induced as an anomaly; an infinity
multiplied by an infinitesimal factor. The infinity comes from the singularity
at the edge of the eigenvalue distribution of the Neumann matrix, while the
infinitesimal factor from the violation of the equation of motion of the
fluctuation modes due to the regularization for the infinity. However, the
transversality condition cannot be obtained even if we take into account the
anomaly contribution.Comment: 19 pages, LaTeX2
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
The Perturbative Spectrum of the Dressed Sliver
We analyze the fluctuations of the dressed sliver solution found in a
previous paper, hep-th/0311198, in the operator formulation of Vacuum String
Field Theory. We derive the tachyon wave function and then analyze the higher
level fluctuations. We show that the dressing is responsible for implementing
the transversality condition on the massless vector. In order to consistently
deal with the singular mode we introduce a string midpoint regulator and
we show that it is possible to accommodate all the open string states among the
solutions to the linearized equations of motion. We finally show how the
dressing can give rise to the correct ratio between the energy density of the
dressed sliver and the brane tension computed via the three-tachyons-coupling.Comment: 52 pages, v2: comment added in sec. 5, v3: one appendix added,
comments added in introduction and conclusion, to appear on PR
Higher Level Open String States from Vacuum String Field Theory
We construct massive open string states around a classical solution in the
oscillator formulation of Vacuum String Field Theory. In order for the correct
mass spectrum to be reproduced, the projection operators onto the modes of the
left- and right-half of the string must have an anomalous eigenvalue 1/2, and
the massive states are constructed using the corresponding eigenvector. We
analyze numerically the projection operators by regularizing them to finite
size matrices and confirm that they indeed have eigenvalue 1/2. Beside the
desired massive states, we have spurious massive as well as massless states,
which are infinitely degenerate. We show that these unwanted states can be
gauged away.Comment: 16 pages, no figures, LaTeX, v2:minor correction
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
Star Algebra Projectors
Surface states are open string field configurations which arise from Riemann
surfaces with a boundary and form a subalgebra of the star algebra. We find
that a general class of star algebra projectors arise from surface states where
the open string midpoint reaches the boundary of the surface. The projector
property of the state and the split nature of its wave-functional arise because
of a nontrivial feature of conformal maps of nearly degenerate surfaces.
Moreover, all such projectors are invariant under constant and opposite
translations of their half-strings. We show that the half-string states
associated to these projectors are themselves surface states. In addition to
the sliver, we identify other interesting projectors. These include a butterfly
state, which is the tensor product of half-string vacua, and a nothing state,
where the Riemann surface collapses.Comment: 65 pages, 23 figures, LaTe
Level Truncated Tachyon Potential in Various Gauges
New gauge fixing condition with single gauge parameter proposed by the
authors is applied to the level truncated analysis of tachyon condensation in
cubic open string field theory. It is found that the only one real non-trivial
extremum persists to appear in the well-defined region of the gauge parameter,
while the other solutions are turned out to be gauge-artifacts. Contrary to the
previously known pathology in the Feynman-Siegel gauge, tachyon potential is
remarkably smooth enough around Landau-type gauge.Comment: 13 pages, 5 figures. For associated movie files, see
http://hep1.c.u-tokyo.ac.jp/~kato/sft
Construction of the Vacuum String Field Theory on a non-BPS Brane
In the framework of the Sen conjectures a construction of vacuum superstring
field theory on a non-BPS brane is discussed. A distinguished feature of this
theory is a presence of a ghost kinetic operator mixing GSO+/- sectors. A
candidate for such kinetic operator with zero cohomology is discussed.Comment: expression for the pure ghost kinetic operator corrected, Comments
added; 21 pages, 1 figure, LaTeX 2
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