158 research outputs found
The boundary state for a class of analytic solutions in open string field theory
We construct a boundary state for a class of analytic solutions in the
Witten's open string field theory. The result is consistent with the property
of the zero limit of a propagator's length, which was claimed in [19]. And we
show that our boundary state becomes expected one for the perturbative vacuum
solution and the tachyon vacuum solution. We also comment on possible presence
of multi-brane solutions and ghost brane solutions from our boundary state.Comment: 19 pages, 2 figure
Superstring field theory equivalence: Ramond sector
We prove that the finite gauge transformation of the Ramond sector of the
modified cubic superstring field theory is ill-defined due to collisions of
picture changing operators.
Despite this problem we study to what extent could a bijective classical
correspondence between this theory and the (presumably consistent)
non-polynomial theory exist. We find that the classical equivalence between
these two theories can almost be extended to the Ramond sector: We construct
mappings between the string fields (NS and Ramond, including Chan-Paton factors
and the various GSO sectors) of the two theories that send solutions to
solutions in a way that respects the linearized gauge symmetries in both sides
and keeps the action of the solutions invariant. The perturbative spectrum
around equivalent solutions is also isomorphic.
The problem with the cubic theory implies that the correspondence of the
linearized gauge symmetries cannot be extended to a correspondence of the
finite gauge symmetries. Hence, our equivalence is only formal, since it
relates a consistent theory to an inconsistent one. Nonetheless, we believe
that the fact that the equivalence formally works suggests that a consistent
modification of the cubic theory exists. We construct a theory that can be
considered as a first step towards a consistent RNS cubic theory.Comment: v1: 24 pages. v2: 27 pages, significant modifications of the
presentation, new section, typos corrected, references adde
An Algorithm for constructing Hjelmslev planes
Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations
of projective planes and affine planes. We present an algorithm for
constructing a projective Hjelmslev planes and affine Hjelsmelv planes using
projective planes, affine planes and orthogonal arrays. We show that all
2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv
planes can be constructed in this way. As a corollary it is shown that all
2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective
Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014,
Springer Proceedings in Mathematics & Statistics 13
Level truncation analysis of exact solutions in open string field theory
We evaluate vacuum energy density of Schnabl's solution using the level
truncation calculation and the total action including interaction terms. The
level truncated solution provides vacuum energy density expected both for
tachyon vacuum and trivial pure gauge. We discuss the role of the phantom term
to reproduce correct vacuum energy.Comment: 11 pages, 6 figures,v2: 1 figure replace
Comments on superstring field theory and its vacuum solution
We prove that the NS cubic superstring field theories are classically
equivalent, regardless of the choice of Y_{-2} in their definition, and
illustrate it by an explicit evaluation of the action of Erler's solution. We
then turn to examine this solution. First, we explain that its cohomology is
trivial also in the Ramond sector. Then, we show that the boundary state
corresponding to it is identically zero. We conclude that this solution is
indeed a closed string vacuum solution despite the absence of a tachyon field
on the BPS D-brane.Comment: 15 pages, 1 figure; v2. typos correcte
Ghost story. III. Back to ghost number zero
After having defined a 3-strings midpoint-inserted vertex for the bc system,
we analyze the relation between gh=0 states (wedge states) and gh=3 midpoint
duals. We find explicit and regular relations connecting the two objects. In
the case of wedge states this allows us to write down a spectral decomposition
for the gh=0 Neumann matrices, despite the fact that they are not commuting
with the matrix representation of K1. We thus trace back the origin of this
noncommutativity to be a consequence of the imaginary poles of the wedge
eigenvalues in the complex k-plane. With explicit reconstruction formulas at
hand for both gh=0 and gh=3, we can finally show how the midpoint vertex avoids
this intrinsic noncommutativity at gh=0, making everything as simple as the
zero momentum matter sector.Comment: 40 pages. v2: typos and minor corrections, presentation improved in
sect. 4.3, plots added in app. A.1, two refs added. To appear in JHE
Ghost story. II. The midpoint ghost vertex
We construct the ghost number 9 three strings vertex for OSFT in the natural
normal ordering. We find two versions, one with a ghost insertion at z=i and a
twist-conjugate one with insertion at z=-i. For this reason we call them
midpoint vertices. We show that the relevant Neumann matrices commute among
themselves and with the matrix representing the operator K1. We analyze the
spectrum of the latter and find that beside a continuous spectrum there is a
(so far ignored) discrete one. We are able to write spectral formulas for all
the Neumann matrices involved and clarify the important role of the integration
contour over the continuous spectrum. We then pass to examine the (ghost) wedge
states. We compute the discrete and continuous eigenvalues of the corresponding
Neumann matrices and show that they satisfy the appropriate recursion
relations. Using these results we show that the formulas for our vertices
correctly define the star product in that, starting from the data of two ghost
number 0 wedge states, they allow us to reconstruct a ghost number 3 state
which is the expected wedge state with the ghost insertion at the midpoint,
according to the star recursion relation.Comment: 60 pages. v2: typos and minor improvements, ref added. To appear in
JHE
Solutions from boundary condition changing operators in open string field theory
We construct analytic solutions of open string field theory using boundary
condition changing (bcc) operators. We focus on bcc operators with vanishing
conformal weight such as those for regular marginal deformations of the
background. For any Fock space state phi, the component string field
of the solution Psi exhibits a remarkable factorization property: it is given
by the matter three-point function of phi with a pair of bcc operators,
multiplied by a universal function that only depends on the conformal weight of
phi. This universal function is given by a simple integral expression that can
be computed once and for all. The three-point functions with bcc operators are
thus the only needed physical input of the particular open string background
described by the solution. We illustrate our solution with the example of the
rolling tachyon profile, for which we prove convergence analytically. The form
of our solution, which involves bcc operators instead of explicit insertions of
the marginal operator, can be a natural starting point for the construction of
analytic solutions for arbitrary backgrounds.Comment: 21 pages, 1 figure, LaTeX2e; v2: minor changes, version published in
JHE
A Simple Analytic Solution for Tachyon Condensation
In this paper we present a new and simple analytic solution for tachyon
condensation in open bosonic string field theory. Unlike the B_0 gauge
solution, which requires a carefully regulated discrete sum of wedge states
subtracted against a mysterious "phantom" counter term, this new solution
involves a continuous integral of wedge states, and no regularization or
phantom term is necessary. Moreover, we can evaluate the action and prove Sen's
conjecture in a mere few lines of calculation.Comment: 44 pages
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