Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux

TL;DR

This paper studies how chiral fermions and anomaly cancellation are achieved in six-dimensional supergravity compactified on orbifolds with Wilson lines and flux, revealing new mechanisms involving axions and flux backgrounds.

Contribution

It introduces a detailed analysis of anomaly cancellation via Green-Schwarz terms in orbifold compactifications with flux and Wilson lines, including the role of axions and zero mode wave functions.

Findings

Flux and orbifold singularities produce chiral fermions.

Green-Schwarz mechanism cancels four-dimensional anomalies.

Massless axion couples to gauge fields, enabling anomaly cancellation.

Abstract

We consider six-dimensional supergravity compactified on orbifolds with Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines around the orbifold fixed points, and twisted boundary conditions of matter fields are related to fractional localized flux. Both, orbifold singularities and flux lead to chiral fermions in four dimensions. We show that in addition to the standard bulk and fixed point anomalies the Green-Schwarz term also cancels the four-dimensional anomaly induced by the flux background. The two axions contained in the antisymmetric tensor field both contribute to the cancellation of the four-dimensional anomaly and the generation of a vector boson mass via the Stueckelberg mechanism. An orthogonal linear combination of the axions remains massless and couples to the gauge field in the standard way. Furthermore, we construct convenient expressions for the wave functions of the zero modes and relate their multiplicity and behavior at the fixed points to the bulk flux quanta and the Wilson lines.