We propose a new basis in Witten's open string field theory, in which the star product simplifies considerably. For a convenient choice of gauge, the classical string field equation of motion yields straightforwardly an exact analytic solution that represents the nonperturbative tachyon vacuum. The solution is given in terms of Bernoulli numbers and the equation of motion can be viewed as novel Euler-Ramanujan-type identity. It turns out that the solution is the Euler-Maclaurin asymptotic expansion of a sum over wedge states with certain insertions. This new form is fully regular from the point of view of level truncation. By computing the energy difference between the perturbative and nonperturbative vacua, we prove analytically Sen's first conjecture.e-print archive: http://lanl.arXiv.org/abs/hep-th/0511286 MARTIN SCHNABL Contents

We review the generalized Witten-Nester spinor stability argument for flat domain wall solutions of gravitational theories. Neither the field theory nor the solution need be supersymmetric. Nor is the space-time dimension restricted. We develop the non-trivial extension required for AdS-sliced domain walls and apply this to show that the recently proposed "Janus" solution of Type IIB supergravity is stable non-perturbatively for a broad class of deformations. Generalizations of this solution to arbitrary dimension and a simple curious linear dilaton solution of Type IIB supergravity are byproducts of this work.

In this short letter we present a class of remarkably simple solutions to Witten's open string field theory that describe marginal deformations of the underlying boundary conformal field theory. The solutions we consider correspond to dimension-one matter primary operators that have non-singular operator products with themselves. We briefly discuss application to rolling tachyons.1 For related recent development see [5,6,7,8,9,10]. Nice reviews of string field theory include [11,12].

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. the ψ N term does not contribute to the energy in the ordinary level expansion [1,4], since as a state in the Fock space it vanishes identically.By now the regularization and phantom piece are better understood [2,5,6,7,8,9,10], and there is little doubt that the B 0 gauge solution is for practical purposes nonsingular. Yet, no one has found an adequate definition of the solution-or gauge equivalent alternative-which does not require the regulated sum and phantom piece.In this note, we present an alternative solution for the tachyon vacuum which avoids the above complications. Instead of a discrete sum, the solution involves a continuous integral over wedge states, and no regularization or mysterious phantom term is necessary.Moreover, evaluation of the action and the proof of Sen's conjectures is, in contrast to the B 0 gauge, very straightforward.Broad classes of generalizations of the B 0 gauge solution have been constructed in [11,12,13,14,7]. Note in particular that our new solution is a special case of the solutions considered in [7], though our analysis will be quite different. This paper is organized as follows. After some algebraic and notational preliminaries, in Section 2 we present the new solution for the tachyon vacuum, comment on its structure, and prove the equations of motion. In Sec.2.1 we prove Sen's conjectures, specifically proving the absence of open string states and giving a very simple calculation of the brane tension. In Sec.2.2 we comment on the relation between pure gauge solutions and the phantom piece, and in Sec.2.3 we compute the closed string tadpole and demonstrate that it vanishes. In Section 3 we investigate the energy of the new vacuum in level truncation. As a warmup exercise, in Sec.3.1 we consider the L 0 level expansion. Due to the remarkable simplicity of our solution, we can solve the L 0 expansion exactly; we resum the expansion to confirm Sen's conjecture up to better than one part in 10 million. In Sec.3.2 we consider the "true" level expansion in terms of eigenstates of L 0 . Surprisinglyunlike the Siegel gauge or B 0 gauge tachyon condensates-we find that the expansion for the energy does not converge. In order to understand this phenomenon, in section Sec.3.3we consider a toy model of our solution where the L 0 level expansion, though divergent, can be solved exactly. In the end, we are able to resum the L 0 expansion of our solution and confirm Sen's conjecture to better than 99%. We end with some discussion.

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.