Half-string oscillator approach to string field theory

Abstract

In this letter we present an operator formalism for Closed String Field Theory based on closed half-strings. Our results indicate that the restricted polyhedra of the classical non-polynomial string field theory, can be represented as traces of infinite matrices, with operator insertions that reparametrise the half-strings.

Continuous half-string representation of string field theory

“…The half-string formalism in the sliver basis was studied in [28], while the half-string formalism of [26] is actually the half-string in the butterfly basis [41]. We end the section by incorporating the zero mode and the ghost sector into the formalism, enabling us to calculate the normalization of the vertices.…”

“…The subgroup parameterized by −π/2 < θ < π/2, can be parametrized as 25) where −∞ < t < ∞. Now the star-multiplication rule simplifies to a linear relation 26) and the anomaly is hidden at t = ±∞. In this parameterization all gauge transformations are generated by infinitesimal gauge transformations Λ.…”

“…As a byproduct of the new interest in string field theory, further ways to simplify the star product were developed, most notably the half-string formulation [26,27,19,28], spectroscopy of the three-vertex [29,30], and the Moyal formulations [31]- [35]. Different subalgebras of the star product were recognized, usually belonging to the subalgebra of (shifted) squeezed states.…”

“…In [26] the half-string representation was described using discrete half-string oscillator. We suggest using a continuous set of oscillators.…”

On surface states and star-subalgebras in string field theory

“…The fact that they are rank one projectors means that their wave function factorizes to g(l)g(r), where l, r stand for the degrees of freedom on the left and right half strings respectively and g is some functional of these degrees of freedom. In the half-string formalism [32,33,34,35] we can represent such states by a matrix…”