Normal ordering and boundary conditions for fermionic string coordinates

TL;DR

This paper develops a consistent normal ordering for fermionic open string coordinates considering boundary conditions and background fields, revealing endpoint discontinuities and boundary effects on the energy-momentum tensor while maintaining the standard central charge.

Contribution

It introduces a novel normal ordering scheme for fermionic string coordinates that accounts for boundary conditions and background fields, ensuring consistency at string endpoints.

Findings

Normal ordered products exhibit discontinuities at string endpoints.

Boundary conditions affect the energy-momentum tensor at the world-sheet boundary.

The central charge remains unchanged despite boundary modifications.

Abstract

We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy momentum tensor also changes at the world-sheet boundary in such a way that the central charge keeps the standard value at string end points.