Bernoulli Numbers and Multi-brane Solutions in Cubic String Field Theory

Abstract

In a previous paper [arXiv:1901.01681], we presented an analytic construction of multi-brane solutions in cubic open string field theory (CSFT) for any integer brane number. Our $(N+1)$-brane solution is given in the pure-gauge form $\Psi =U{Q}_{\text{B}}{U}^{-1}$ in terms of a unitary string field $U$ which is specified by $[N/2]$ independent real parameters ${\alpha }_k$. We saw that, for various sample values of $N$ $(=2,3,4,5,\cdots )$, ${\alpha }_k$ can be consistently determined by two requirements: The energy density from the action should reproduce that of $(N+1)$-branes, and the EOM of the solution against the solution itself should hold. In this paper, we complete our construction by determining ${\alpha }_k$ satisfying the two requirements for a generic $N$. We find that each ${\alpha }_k$ is given in a closed form by using the Bernoulli numbers. We also present some supplementary results on our solution; the energy density of the solutions determined from its gravitational coupling, and the unitary string field $U$ as an exponential function.

21 pages, no figures

References in corpus (4)

• Comments on Schnabl's analytic solution for tachyon condensation in Witten's open string field theory
• A Simple Analytic Solution for Tachyon Condensation
• Gauge Invariant Overlaps for Classical Solutions in Open String Field Theory
• On Multibrane Solutions in Open String Field Theory

Cited by in corpus (1)

• Winding number for arbitrary integer value in Cubic String Field Theory