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

Algebraic Solutions in Open String Field Theory – a Lightning Review

In this short paper we review basic ideas of string field theory with the emphasis on the recent developments. We show how without much technicalities one can look for analytic solutions to Witten’s open string field theory. This is an expanded version of a talk given by the author over the last year at a number of occasions1 and notably at the conference Selected Topics in Mathematical and Particle Physics in honor of Prof. JiˇrLi Niederle’s 70th birthday

Exact solitons on noncommutative tori

We construct exact solitons on noncommutative tori for the type of actions arising from open string field theory. Given any projector that describes an extremum of the tachyon potential, we interpret the remaining gauge degrees of freedom as a gauge theory on the projective module determined by the tachyon. Whenever this module admits a constant curvature connection, it solves exactly the equations of motion of the effective string field theory. We describe in detail such a construction on the noncommutative tori. Whereas our exact solution relies on the coupling to a gauge theory, we comment on the construction of approximate solutions in the absence of gauge fields.Comment: 22 pages, JHEP style, typos corrected and references improve

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

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

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

Winding Number in String Field Theory

Motivated by the similarity between cubic string field theory (CSFT) and the Chern-Simons theory in three dimensions, we study the possibility of interpreting N=(\pi^2/3)\int(U Q_B U^{-1})^3 as a kind of winding number in CSFT taking quantized values. In particular, we focus on the expression of N as the integration of a BRST-exact quantity, N=\int Q_B A, which vanishes identically in naive treatments. For realizing non-trivial N, we need a regularization for divergences from the zero eigenvalue of the operator K in the KBc algebra. This regularization must at same time violate the BRST-exactness of the integrand of N. By adopting the regularization of shifting K by a positive infinitesimal, we obtain the desired value N[(U_tv)^{\pm 1}]=\mp 1 for U_tv corresponding to the tachyon vacuum. However, we find that N[(U_tv)^{\pm 2}] differs from \mp 2, the value expected from the additive law of N. This result may be understood from the fact that \Psi=U Q_B U^{-1} with U=(U_tv)^{\pm 2} does not satisfy the CSFT EOM in the strong sense and hence is not truly a pure-gauge in our regularization.Comment: 20 pages, no figures; v2: references added, minor change

Yang-Mills Action from Open Superstring Field Theory

We calculate the effective action for nonabelian gauge bosons up to quartic order using WZW-like open superstring field theory. After including level zero and level one contributions, we obtain with 75% accuracy the Yang-Mills quartic term. We then prove that the complete effective action reproduces the exact Yang-Mills quartic term by analytically performing a summation over the intermediate massive states.Comment: 10 page

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