Decay Modes of Unstable Strings in Plane-Wave String Field Theory

TL;DR

This paper investigates decay modes of unstable strings in plane-wave string field theory, revealing conditions under which decay matrix elements vanish or not, and comparing results with gauge theory predictions.

Contribution

It provides a simplified effective interaction vertex for bosonic states and analyzes decay modes, highlighting when decay amplitudes vanish or persist, with implications for the BMN correspondence.

Findings

Decay amplitudes vanish for initial states with two or fewer excitations.

Decay amplitudes generally do not vanish for states with more than two excitations.

Quantitative discrepancies exist between string theory calculations and gauge theory predictions.

Abstract

The cubic interaction vertex of light-cone string field theory in the plane-wave background has a simple effective form when considering states with only bosonic excitations. This simple effective interaction vertex is used in this paper to calculate the three string interaction matrix elements for states of arbitrary bosonic excitation and these results are used to examine certain decay modes on the mass-shell. It is shown that the matrix elements of one string to two string decays involving only bosonic excitations will vanish to all orders in 1/mu on the mass-shell when the number of excitations on the initial string is less than or equal to two, but in general will not vanish when the number of excitations is greater than two. Also, a truncated calculation of the mass-shell matrix elements for one string to three string decays of two excitation states is performed and suggests that these matrix elements do not vanish on the mass-shell. There is, however, a quantitative discrepancy between this last result and its (also non-vanishing) gauge theory prediction from the BMN correspondence.