Singularities in K-space and multi-brane solutions in cubic string field theory

Abstract

In a previous paper [arXiv:1111.2389], we studied the multi-brane solutions in cubic string field theory by focusing on the topological nature of the "winding number" N which counts the number of branes. We found that N can be nontrivial owing to the singularity from the zero-eigenvalue of K of the KBc algebra, and that solutions carrying integer N and satisfying the EOM in the strong sense is possible only for N = 0, ±1. In this paper, we extend the construction of multibrane solutions to |N | ≥ 2. The solutions with N = ±2 is made possible by the fact that the correlator is invariant under a transformation exchanging K with 1/K and hence K = ∞ eigenvalue plays the same role as K = 0. We further propose a method of constructing solutions with |N | ≥ 3 by expressing the eigenvalue space of K as a sum of intervals where the construction for |N | ≤ 2 is applicable.

Analytic construction of multi-brane solutions in cubic string field theory for any brane number

“…Though the configuration (1.2) is a pure-gauge one and formally satisfies the EOM, Q B Ψ + Ψ 2 = 0, (1.5) this is in fact a subtle problem due to the singularity at K = 0. As the requirements on the pure-gauge configuration Ψ (1.2) as a solution, the number of D25-branes Ψ represents and the EOM test of Ψ against itself were examined for various G(K) defining U [5,6,7,8]. For calculating these quantities, we have to regularize the singularity at K = 0.…”

“…The EOM test is also passed, namely, T = 0 in these two cases. It was shown that the origin of non-trivial N in these solutions is the singularity coming from the zero or pole of G(K) at K = 0 [5,6,7,8].…”

“…where the "anomalous terms" A N and B N are expressed in terms of the confluent hypergeometric function 4 as 2 We are taking both the open string coupling constant and the space-time volume equal to one. 3 G(K) should not have zero nor pole at K = ∞ to avoid their additional contribution to N [8]. 4 The confluent hypergeometric function is defined by…”

Taming boundary condition changing operator anomalies with the tachyon vacuum

“…More surprisingly, it is possible to generalize this into an automorphism group of the KBc subalgebra [21]. Applications of this symmetry have been discussed in [13,[20][21][22][23][24][25][26]. Here we show that the automorphisms can be further extended to act on boundary condition changing operators.…”

“…For the purposes of the present discussion we leave these subtleties to the side, and proceed under the assumption that the spectrum of K is real and non-negative. 8 There has been interesting discussion of diffeomorphisms of the spectrum of K which are not homotopic to the identity, generated by the transformation K → 1/K [20]. The resulting automorphisms are singular, and we will not consider them.…”