Abstract:We regulate Witten's open superstring field theory by replacing the picturechanging insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the A ∞ relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.

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.

In this paper we give an exact analytic solution for tachyon condensation in the modified (picture 0) cubic superstring field theory. We prove the absence of cohomology and, crucially, reproduce the correct value for the D-brane tension. The solution is surprising for two reasons: First, the existence of a tachyon vacuum in this theory has not been definitively established in the level expansion. Second, the solution vanishes in the GSO(−) sector, implying a "tachyon vacuum" solution exists even for a BPS D-brane.

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D(p−1)-brane in the string field theory of a Dp-brane, for generic compactification radius. This not only provides a proof of Sen's second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can "reverse" the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.

We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.