Solutions in Bosonic String Field Theory and Higher Spin Algebras in AdS

TL;DR

This paper constructs analytic solutions in open bosonic string field theory linked to higher spin algebras in AdS3, revealing algebraic structures and potential extensions to superstring theory.

Contribution

It introduces a new class of solutions parametrized by higher spin algebra in AdS3, expressed via Bell polynomial generating functions, and explores their algebraic properties and extensions.

Findings

Solutions expressed in terms of Bell polynomial products

Realization of $W_ abla$ and higher spin algebras

Potential extensions to superstring theory

Abstract

We find a class of analytic solutions in open bosonic string field theory, parametrized by the chiral copy of higher spin algebra in $AdS_3$. The solutions are expressed in terms of the generating function for the products of Bell polynomials in derivatives of bosonic space-time coordinates $X^m(z)$ of the open string, which form is determined in this work. The products of these polynomials form a natural operator algebra realizations of $W_\infty$ (area-preserving diffeomorphisms), enveloping algebra of SU(2) and higher spin algebra in $AdS_3$. The class of SFT solutions found can, in turn, be interpreted as the "enveloping of enveloping", or the enveloping of $AdS_3$ higher spin algebra. We also discuss the extensions of this class of solutions to superstring theory and their relations to higher spin algebras in higher space-time dimensions.