Strings on Orbifold Lines

TL;DR

The paper studies RR discrete torsion variants on Type II orbifold lines, showing RR fluxes are encoded in twisted sector fields and are naturally captured by equivariant K-theory rather than ordinary cohomology. It derives the tension and NSNS charge Q(F) of the orbifold lines as a quadratic function of the twisted field F, namely Q(F) = 4F^2 − 1/16, using a combination of low-energy effective action, string creation (Hanany–Witten) arguments, and a self-intersection/K-theory perspective. The analysis reveals how D-brane domain walls induce discrete jumps in F with magnitudes Delta F_p = 2^{-p/2} for fractional Dp-branes, and identifies a non-dynamical twisted RR vector A in two dimensions whose flux is tied to the twisted brane spectrum. Overall, the work demonstrates that K-theory corrections modify cohomological discrete torsion results, clarifies the relation between RR fluxes at infinity and NSNS charges, and provides a consistent, duality-checkable framework for RR-NSNS couplings in orbifold backgrounds.

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.

Figures (1)

• Figure 1: String creation when two D0 branes are crossing on an orbifold line. The wavy line is the newly created string.