Physical states for non-linear $SO(N)$ strings

TL;DR

This paper investigates low-lying physical states in a superstring theory with a non-linear $SO(N)$ superconformal algebra, highlighting the discrete nature of states and providing a BRST operator construction for the $N=3$ case.

Contribution

It introduces a new analysis of physical states in a non-linear $SO(N)$ superconformal algebra-based superstring theory and constructs the BRST operator for the $N=3$ case.

Findings

All physical states are discrete, similar to one-scalar bosonic strings.

Constructed the BRST operator explicitly for the $N=3$ case.

Identified the unique features of the $SO(N)$ extended superconformal algebra.

Abstract

We study some low-lying physical states in a superstring theory based on the quadratically non-linear $SO(N)$--extended superconformal algebra. In the realisation of the algebra that we use, all the physical states are discrete, analogous to the situation in a one-scalar bosonic string. The BRST operator for the $N=3$ case needs to be treated separately, and its construction is given here.