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

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

Schnabl's L_0 Operator in the Continuous Basis

Following Schnabl's analytic solution to string field theory, we calculate the operators ${\cal L}_0,{\cal L}_0^\dagger$ for a scalar field in the continuous $\kappa$ 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

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

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

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

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

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

The off-shell Veneziano amplitude in Schnabl gauge

We give a careful definition of the open string propagator in Schnabl gauge and present its worldsheet interpretation. The propagator requires two Schwinger parameters and contains the BRST operator. It builds surfaces by gluing strips of variable width to the left and to the right of off-shell states with contracted or expanded local frames. We evaluate explicitly the four-point amplitude of off-shell tachyons. The computation involves a subtle boundary term, crucial to enforce the correct exchange symmetries. Interestingly, the familiar on-shell physics emerges even though string diagrams produce Riemann surfaces more than once. Off-shell, the amplitudes do not factorize over intermediate on-shell states.Comment: 48 pages, 10 figures. v2:acknowledgments adde