Marginal and Scalar Solutions in Cubic Open String Field Theory

Abstract

We find marginal and scalar solutions in cubic open string field theory by using left-right splitting properties of a delta function. The marginal solution represents a marginal deformation generated by a U(1) current, and it is a generalized solution of the Wilson lines one given by the present authors. The scalar solution has a well-defined universal Fock space expression, and it is expressed as a singular gauge transform of the trivial vacuum. The expanded theory around it is unable to be connected with the original theory by the string field redefinition. Errors in hep-th/0112124 are corrected in this paper. * inated in a delta function, and so their Fock space expressions are ill-defined. On the other hand, our marginal and scalar solutions have well-defined Fock space expressions, and the marginal solutions contain the solution corresponding to deformations of D-brane positions.This paper is organized as follows. In sec. 2, we prove the splitting properties of a delta function. In sec. 3, we construct general marginal solutions generated by a U(1) current. We construct a scalar solution which represents a non-trivial background in sec. 4. We give summary and discussions in sec. 5. We present some detail calculations in the appendix. Splitting Properties of Delta FunctionWe define a delta function as follows,

BCFT moduli space in level truncation

“…Concrete examples of these 'far' solutions in OSFT have been presented in [10] and in [5] building on [11][12][13][14][15]. It is therefore an important question whether we can find these solutions in Siegel gauge as well.…”

Marginal Deformations and Closed String Couplings in Open String Field Theory

“…* We denote the complex coordinate w in refs. [3,4] by z. † We can show that Ψ 0 (λ) obeys the equation of motion by using the commutation relation 4) and the following properties…”

“…As discussed in ref. [3], the action for the quantum fluctuation is transformed to the original form by the string field redefinition:…”

“…For example, the tachyon vacuum solution should be obtained as a kind of large gauge transformations of the perturbative vacuum as proposed in ref. [3].…”

“…[3,4]. In section 3 we will derive oscillator expression of the the on-shell closed string coupling to the open string field.…”