Normal ordering and non(anti)commutativity in open super strings

TL;DR

This paper explores nonanticommutativity in open super strings influenced by a background field, employing a novel normal ordering approach that clarifies the underlying algebraic structures and aligns with existing literature.

Contribution

It introduces a new normal ordering method to derive mode algebra and nonanticommutative structures in open super strings, providing clearer insights than previous approaches.

Findings

Derived fermionic string coordinate anticommutator using new normal ordering

Revealed nonanticommutative structure in fermionic coordinates

Results consistent with existing literature

Abstract

Nonanticommutativity in an open super string moving in the presence of a background antisymmetric tensor field $\mathcal{B}_{\mu \nu}$ is investigated in a conformal field theoretic approach, leading to nonanticommutative structures. In contrast to several discussions, in which boundary conditions are taken as Dirac constraints, we first obtain the mode algebra by using the newly proposed normal ordering, which satisfies both equations of motion and boundary conditions. Using these the anticommutator among the fermionic string coordinates is obtained. Interestingly, in contrast to the bosonic case, this new normal ordering plays an important role in uncovering the underlying nonanticommutative structure between the fermionic string coordinates. We feel that our approach is more transparent than the previous ones and the results we obtain match with the existing results in the literature.