638 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
Star Algebra Spectroscopy
The spectrum of the infinite dimensional Neumann matrices M^{11}, M^{12} and
M^{21} in the oscillator construction of the three-string vertex determines key
properties of the star product and of wedge and sliver states. We study the
spectrum of eigenvalues and eigenvectors of these matrices using the derivation
K_1 = L_1 + L_{-1} of the star algebra, which defines a simple infinite matrix
commuting with the Neumann matrices. By an exact calculation of the spectrum of
K_1, and by consideration of an operator generating wedge states, we are able
to find analytic expressions for the eigenvalues and eigenvectors of the
Neumann matrices and for the spectral density. The spectrum of M^{11} is
continuous in the range [-1/3, 0) with degenerate twist even and twist odd
eigenvectors for every eigenvalue except for -1/3.Comment: LaTeX, 30 pages, 2 figure
Some exact results on the matter star-product in the half-string formalism
We show that the D25 sliver wavefunction, just as the D-instanton sliver,
factorizes when expressed in terms of half-string coordinates. We also
calculate analytically the star-product of two zero-momentum eigenstates of
using the vertex in the oscillator basis, thereby showing that the
star-product in the matter sector can indeed be seen as multiplication of
matrices acting on the space of functionals of half strings. We then use the
above results to establish that the matrices , conjectured by
Rastelli, Sen and Zwiebach to be left and right projectors on the sliver, are
indeed so.Comment: 27 pages; footnote adde
Ghost Kinetic Operator of Vacuum String Field Theory
Using the data of eigenvalues and eigenvectors of Neumann matrices in the
3-string vertex, we prove analytically that the ghost kinetic operator of
vacuum string field theory obtained by Hata and Kawano is equal to the ghost
operator inserted at the open string midpoint. We also comment on the values of
determinants appearing in the norm of sliver state.Comment: 19 pages, 1 figure, lanlmac; v2: typos correcte
Siegel Gauge in Vacuum String Field Theory
We study the star algebra of ghost sector in vacuum string field theory
(VSFT). We show that the star product of two states in the Siegel gauge is BRST
exact if we take the BRST charge to be the one found in hep-th/0108150, and the
BRST exact states are nil factors in the star algebra. By introducing a new
star product defined on the states in the Siegel gauge, the equation of motion
of VSFT is characterized as the projection condition with respect to this new
product. We also comment on the comma form of string vertex in the ghost
sector.Comment: 13 pages, lanlmac; v3: comment adde
The Spectrum of the Neumann Matrix with Zero Modes
We calculate the spectrum of the matrix M' of Neumann coefficients of the
Witten vertex, expressed in the oscillator basis including the zero-mode a_0.
We find that in addition to the known continuous spectrum inside [-1/3,0) of
the matrix M without the zero-modes, there is also an additional eigenvalue
inside (0,1). For every eigenvalue, there is a pair of eigenvectors, a
twist-even and a twist-odd. We give analytically these eigenvectors as well as
the generating function for their components. Also, we have found an
interesting critical parameter b_0 = 8 ln 2 on which the forms of the
eigenvectors depend.Comment: 25+1 pages, 3 Figures; typos corrected and some comments adde
Ratio of Tensions from Vacuum String Field Theory
We show analytically that the ratio of the norm of sliver states agrees with
the ratio of D-brane tensions. We find that the correct ratio appears as a
twist anomaly.Comment: 13 pages, lanlmac; version to appear in JHE
Chan-Paton factors and Higgsing from Vacuum String Field Theory
We give a description of open strings stretched between N parallel D-branes
in VSFT. We show how higgsing is generated as the branes are displaced: the
shift in the mass formula for on-shell states stretched between different
branes is due to a twist anomaly, a contribution localized at the midpoint.Comment: 20 pages, JHEP clas
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
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
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