Strings on Orbifold Lines

TL;DR

This paper classifies BPS discrete torsion variants on orbifold lines using equivariant K-theory, revealing how their tensions and charges depend on an integral electric field, with implications for string theory corrections.

Contribution

It introduces a K-theoretic classification of torsion variants on orbifold lines and computes their physical properties as functions of an integral electric field.

Findings

Torsion variants are classified by an integral electric field F.

Tension and NSNS charge depend on the value of F.

8 units of F are invisible for IIA, 16 for IIB at infinity.

Abstract

The orbifold lines IIA/I_8 and IIB/$I_8 (-1)^{F_L} possess BPS discrete torsion variants which carry fundamental string (NSNS) charge. We show that these variants are actually classified by an integral electric field F from the twisted RR sector, and compute their tension and NSNS charge as a function of F. The analysis employs equivariant K-theory and the string creation phenomenon. The K-theory results demonstrate the corrections to cohomology in the case of torsion; it is found that 8 units of F are invisible at transverse infinity for IIA, and correspondingly 16 units for IIB.