Analytical construction of a nonperturbative vacuum for the open bosonic string

Abstract

Using analytical methods, a nonperturbative vacuum is constructed recursively in the field theory for the open bosonic string. Evidence suggests it corresponds to the Lorentz-invariant end point of tachyon condensation on a D25-brane. The corresponding string field is a twisted squeezed state.

Classical solutions in string field theory around the tachyon vacuum

“…As pointed out in the introduction, there are two ways of doing this. One method [10] gives a description of this state in terms of matter Virasoro generators and the other method [16] describes this state in terms of the oscillators of the matter fields. Since the second method can be generalized to describe lump solutions, we first describe this method in detail, and then compare this with the first description.…”

“…where CJ = e 27 ™/ 3 , U and C are regarded as matrices with indices running over ra,n > 1, 16) and U satisfies ((B.17))…”

“…[16] (referred to as |7m) in the introduction) after suitable correction to the normalization factor. From eq.…”

“…The ratios of tensions of various D-branes, requiring evaluation of determinants of infinite dimensional matrices, are calculated numerically and are in very good agreement with the known results. Cubic open string field theory [1] has turned out to be a powerful tool in studying various conjectures [2,3] about tachyon condensation on bosonic Dbranes [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. One aspect of the tachyon conjectures that remains to be confirmed is the expected absence of physical open string excitations around the tachyon vacuum.…”

“…For reasons which will become clear later, we identify the matter part S m of the sliver, with suitable normalization, as the matter part of the solution describing the D25-brane. More recently, Kostelecky and Potting [16] investigated solutions of the equation \I/ m * m \I/ m = \I> m by using an explicit representation of the *-product in terms of Neumann coefficients for free (matter) scalars. In addition to the matter part of the identity X, they found one nontrivial solution Tm.…”