On the deep superstring spectrum

TL;DR

This paper introduces a covariant algebraic method to construct physical state trajectories in superstring theory, leveraging orthosymplectic algebra to systematically generate states in both NS and R sectors.

Contribution

It develops a novel covariant framework using orthosymplectic algebra to construct superstring trajectories, extending previous bosonic string techniques to superstrings.

Findings

Constructed trajectories in NS sector using lowest weight states.

Extended the method to R sector with additional states.

Demonstrated examples of higher trajectories using algebraic operators.

Abstract

We propose a covariant method of constructing entire trajectories of physical states in superstring theory in the critical dimension. It is inspired by a recently developed covariant technology of excavating bosonic string trajectories, that is facilitated by the observation that the Virasoro constraints can be written as linear combinations of lowering operators of a bigger algebra, namely a symplectic algebra, which is Howe dual to the spacetime Lorentz algebra. For superstrings, it is the orthosymplectic algebra that appears instead, with its lowest weight states forming the simplest class of physical trajectories in the NS sector. To construct the simplest class in the R sector, the lowest weight states need to be supplemented with other states, which we determine. Deeper trajectories are then constructed by acting with suitable combinations of the raising operators of the orthosymplectic algebra, which we illustrate with several examples.