33 research outputs found
On the validity of the solution of string field theory
We analyze the realm of validity of the recently found tachyon solution of cubic string field theory. We find that the equation of motion holds in a non trivial way when this solution is contracted with itself. This calculation is needed to conclude the proof of Sen's first conjecture. We also find that the equation of motion holds when the tachyon or gauge solutions are contracted among themselves
Universal regularization for string field theory
We find an analytical regularization for string field theory calculations. This regularization has a simple geometric meaning on the worldsheet, and is therefore universal as level truncation. However, our regularization has the added advantage of being analytical. We illustrate how to apply our regularization to both the discrete and continuous basis for the scalar field and for the bosonized ghost field, both for numerical and analytical calculations. We reexamine the inner products of wedge states, which are known to differ from unity in the oscillator representation in contrast to the expectation from level truncation. These inner products describe also the descent relations of string vertices. The results of applying our regularization strongly suggest that these inner products indeed equal unity. We also revisit Schnabl's algebra and show that the unwanted constant vanishes when using our regularization even in the oscillator representation
Schnabls L0 operator in the continuous basis
Following Schnabl's analytic solution to string field theory, we calculate the operators for a scalar field in the continuous basis. We find an explicit and simple expression for them that further simplifies for their sum, which is block diagonal in this basis. We generalize this result for the bosonized ghost sector, verify their commutation relation and relate our expressions to wedge state representations
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
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
Schnabl's L_0 Operator in the Continuous Basis
Following Schnabl's analytic solution to string field theory, we calculate
the operators for a scalar field in the
continuous basis. We find an explicit and simple expression for them
that further simplifies for their sum, which is block diagonal in this basis.
We generalize this result for the bosonized ghost sector, verify their
commutation relation and relate our expressions to wedge state representations.Comment: 1+16 pages. JHEP style. 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
On the validity of the solution of string field theory
We analyze the realm of validity of the recently found tachyon solution of
cubic string field theory. We find that the equation of motion holds in a non
trivial way when this solution is contracted with itself. This calculation is
needed to conclude the proof of Sen's first conjecture. We also find that the
equation of motion holds when the tachyon or gauge solutions are contracted
among themselves.Comment: JHEP style, 9+1 pages. Typos correcte
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
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