We consider bosonic open string field theory in marginally deformed backgrounds, which is obtained by expanding the string field around the identity-based solutions associated with marginal deformations. We find a new set of string fields which satisfies the KBc algebra, but the nilpotent kinetic operator is that of the theory expanded around the identity-based marginal solution. By use of these string fields, we construct the tachyon vaccum solution in marginally deformed backgrounds. The vacuum energy density is equivalent to that of the tachyon vacuum without marginal deformations.The gauge invariant overlap is changed according to the effect of marginal deformations, as expected from known results in CFT. These results suggest that the vacuum energy is zero for the identity-based marginal solutions in the original theory.1 typeset using P T P T E X.cls Ver.0.9

We construct the homotopy operators for the BRST operator in the theory around the identity-based solutions, which are believed to represent the tachyon vacuum in cubic bosonic open string field theory. Using the homotopy operators, we find that the one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances, which are included in the BRST operator. We also revisit the cohomology problem, which was solved earlier without the homotopy operators.Comment: 16 pages, LaTeX with PTPTeX.cls;v2: comments and footnotes adde

We construct tachyon vacuum and half-brane solutions, using an extension of KBc algebra, in the theory around a type of identity-based marginal solutions in modified cubic superstring field theory. With explicit computations, we find that their vacuum energies are the same as those of corresponding solutions around the original theory. It implies that the vacuum energy for the identity-based marginal solution vanishes although straightforward computation of it is subtle. We also evaluate the gauge invariant overlaps for those nontrivial solutions. The values for them are deformed according to the marginal solution in the same way as the case of bosonic string field theory.

We construct a class of nilpotent operators using the BRST current and ghost fields in superstring theory. The operator can be realized in cubic superstring field theory as a kinetic operator in the background of an identity-based solution. For a particular type of the deformed BRST operators, we find a homotopy operator and discuss its relationship to the cohomology in a similar way to the bosonic case, which has been elaborated by the authors.

We consider one-loop vacuum energy at the tachyon vacuum in cubic bosonic open string field theory. The BRST operator Q l in the theory around an identity-based solution is believed to represent a kinetic operator at the tachyon vacuum. Using homotopy operators for Q l , we find that one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances. This result can be interpreted as support for the annihilation of D-branes at the tachyon vacuum even in the quantum theory. Keywords:The tachyon vacuum; homotopy operators; the one-loop vacuum energy. IntroductionCubic open string field theory has classical solutions describing the tachyon vacuum. The classical vacuum energy cancels a D-brane tension and the BRST cohomology becomes vanishing at the tachyon vacuum.2,3 However, these subjects have so far been studied mainly in classical aspects of string field theory. The purpose of this study 1 is to investigate quantum theoretical properties at the tachyon vacuum. The BRST operators are able to include moduli such as interbrane distances at the perturbative string vacuum. However, after the tachyon condensation, the vacuum energy should be independent of such moduli even in quantum theory.Here, we will demonstrate that a one-loop vacuum amplitude is independent of interbrane distances at the tachyon vacuum. To calculate the vacuum amplitude, we adopt identity-based solutions as the tachyon vacuum solution, and we construct homotopy operators for the BRST operator around the solution. One-Loop Vacuum Energy and CohomologyWe consider bosonic open string field theory with a midpoint interaction. An exact classical solution of the equation of motion was constructed from half-string operators and the identity string field I. 4 The classical solution Ψ 0 includes an arbitrary * This talk is based on the work 1 in collaboration with I. Kishimoto and T. Takahashi.