Bosonization and Fermionization of the Superstring Oscillators

TL;DR

This paper explores the mathematical transformations between bosonic and fermionic oscillators in superstring theory, analyzing their conditions, dualities, and effects on physical states within a covariant framework.

Contribution

It introduces conditions on Grassmannian matrices for bosonization and fermionization of superstring oscillators, including their adjoints and T-duality properties.

Findings

Derived conditions for oscillator transformations.

Analyzed T-duality effects on matrices.

Studied impact on mass operators and states.

Abstract

In this manuscript we consider the transformations of the oscillators of the bosonic fields of the superstring in terms of the fermions oscillators and vice versa. We demand the exchange of the commutation and anti-commutation relations of the oscillators. Therefore, we obtain some conditions on the Grassmannian matrices that appear in these transformations. We observe that there are several methods to obtain these conditions. In addition, adjoints of the matrix elements and $T$-duality of these matrices will be obtained. The effects of this bosonization and fermionization on the mass operators and on some massless states will be studied. The covariant formalism will be used and hence we consider both the matter parts and the ghost parts of the superstring theory.