String non(anti)commutativity for Neveu-Schwarz boundary conditions

TL;DR

This paper investigates how non(anti)commutativity arises in superstring theory with Neveu-Schwarz boundary conditions, emphasizing the role of boundary conditions and their impact on the super constraint algebra's closure.

Contribution

It introduces a novel approach to analyze string non(anti)commutativity by focusing on boundary conditions rather than constraints, and explores implications for superstring consistency.

Findings

Non(anti)commutativity is linked to boundary conditions in superstring theory.

Dirichlet and Neumann boundary conditions are required at opposite ends for antiperiodic bosonic variables.

Derived structures ensure the closure of the super constraint algebra.

Abstract

The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables $X^{\mu}$ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.