Proof of vanishing cohomology at the tachyon vacuum

We prove Sen's third conjecture that there are no on-shell perturbative excitations of the tachyon vacuum in open bosonic string field theory. The proof relies on the existence of a special state A, which, when acted on by the BRST operator at the tachyon vacuum, gives the identity. While this state was found numerically in Feynman-Siegel gauge, here we give a simple analytic expression.Comment: 19 pages, 4 figures; v2: references adde

Generating Erler-Schnabl-type Solution for Tachyon Vacuum in Cubic Superstring Field Theory

We study a new set of identity-based solutions to analyze the problem of tachyon condensation in open bosonic string field theory and cubic superstring field theory. Even though these identity-based solutions seem to be trivial, it turns out that after performing a suitable gauge transformation, we are left with the known Erler-Schnabl-type solutions which correctly reproduce the value of the D-brane tension. This result shows explicitly that how a seemingly trivial solution can generate a non-trivial configuration which precisely represents to the tachyon vacuum.Comment: 22 pages, references added, appendix added, 2 subsections adde

Boundary State from Ellwood Invariants

Boundary states are given by appropriate linear combinations of Ishibashi states. Starting from any OSFT solution and assuming Ellwood conjecture we show that every coefficient of such a linear combination is given by an Ellwood invariant, computed in a slightly modified theory where it does not trivially vanish by the on-shell condition. Unlike the previous construction of Kiermaier, Okawa and Zwiebach, ours is linear in the string field, it is manifestly gauge invariant and it is also suitable for solutions known only numerically. The correct boundary state is readily reproduced in the case of known analytic solutions and, as an example, we compute the energy momentum tensor of the rolling tachyon from the generalized invariants of the corresponding solution. We also compute the energy density profile of Siegel-gauge multiple lump solutions and show that, as the level increases, it correctly approaches a sum of delta functions. This provides a gauge invariant way of computing the separations between the lower dimensional D-branes.Comment: v2: 63 pages, 14 figures. Major improvements in section 2. Version published in JHE

Marginal deformations in string field theory

We describe a method for obtaining analytic solutions corresponding to exact marginal deformations in open bosonic string field theory. For the photon marginal deformation we have an explicit analytic solution to all orders. Our construction is based on a pure gauge solution where the gauge field is not in the Hilbert space. We show that the solution itself is nevertheless perfectly regular. We study its gauge transformations and calculate some coefficients explicitly. Finally, we discuss how our method can be implemented for other marginal deformations.Comment: 23 pages. v2: Some paragraphs improved, typos corrected, ref adde

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

Non-linear analysis of two-layer timber beams considering interlayer slip and uplift

A new mathematical model and its finite element formulation for the non-linear analysis of mechanical behaviour of a two-layer timber planar beam is presented. A modified principle of virtual work is employed in formulating the finite element method. The basic unknowns are strains. The following assumptions are adopted in the mathematical model: materials are taken to be non-linear and can differ from layer to layer; interacting shear and normal contact tractions between layers are derived from the non-linear shear contact traction-slip and the non-linear normal contact traction-uplift characteristics of the connectors; the geometrically linear and materially non-linear Bernoulli's beam theory is assumed for each layer. The formulation is found to be accurate, reliable and computationally effective. The suitability of the theory is validated by the comparison of the numerical solution and the experimental results of full-scale laboratory tests on a simply supported beam. An excellent agreement between measured and calculated results is observed for all load levels. The further objective of the paper is the analysis of the effect of different normal contact traction-uplift constitutive relationships on the kinematic and static quantities in a statically determined and undetermined structure. While the shear contact traction-slip constitutive relationship dictates the deformability of the composite beam and has a substantial influence on most of the static and kinematic quantities of the composite beam, a variable normal contact traction-uplift constitutive relationship is in most cases negligible

Solitons on compact and noncompact spaces in large noncommutativity

We study solutions at the minima of scalar field potentials for Moyal spaces and torii in the large non-commutativity and interprete these solitons in terms of non-BPS D-branes of string theory. We derive a mass spectrum formula linking different D-branes together on quantum torii and suggest that it describes general systems of D-brane bound states extending the D2-D0 one. Then we propose a shape for the effective potential approaching these quasi-stable bound states. We give the gauge symmetries of these systems of branes and show that they depend on the quantum torii representations.Comment: 25 pages, Latex, 1 figure (use epsfig.sty), corrected formul

Tachyon Vacuum Solution in Open String Field Theory with Constant B Field

We show that Schnabl's tachyon vacuum solution is an exact solution of the equation of motion of Witten's open bosonic string field theory in the background of constant antisymmetric two-form field. The action computed at the vacuum solution is given by the Dirac-Born-Infeld factor multiplied to that without the antisymmetric tensor field.Comment: 8 page

Rolling to the tachyon vacuum in string field theory

We argue that the rolling-tachyon solution in cubic OSFT proceeds at late times to precisely the analytic tachyon-vacuum solution constructed by Schnabl. In addition, we demonstrate the relationship between the rolling-tachyon solution and the standard BCFT description by showing that there is a finite gauge transformation which relates the two.Comment: 16 pages, 5 figures, References and comments adde

The Tachyon Potential in the Sliver Frame

We evaluate the tachyon potential in the Schnabl gauge through off-shell computations in the sliver frame. As an application of the results of our computations, we provide a strong evidence that Schnabl's analytic solution for tachyon condensation in open string field theory represents a saddle point configuration of the full tachyon potential. Additionally we verify that Schnabl's analytic solution lies on the minimum of the effective tachyon potential.Comment: v1: 19 pages, 1 figure, 1 table; v2: 20 pages, 1 figure, 2 tables, 1 reference added, comments added; v3: 21 pages, 1 figure, 2 tables, 4 references added, comments adde