Gauge Threshold Corrections for Local Orientifolds

TL;DR

This paper analyzes gauge threshold corrections in local orientifold models with fractional branes, revealing a two-phase gauge coupling running and resolving discrepancies with the Kaplunovsky-Louis formula through 1-loop effects and moduli redefinitions.

Contribution

It provides a detailed CFT construction and computation of gauge threshold corrections for specific orientifold singularities, clarifying the running behavior and non-universality of gauge couplings.

Findings

Two-phase gauge coupling running from winding to string scale and from string to IR.

Discrepancy with Kaplunovsky-Louis formula explained by 1-loop non-universality.

Masses of non-anomalous U(1)s depend on global cycle properties.

Abstract

We study gauge threshold corrections for systems of fractional branes at local orientifold singularities and compare with the general Kaplunovsky-Louis expression for locally supersymmetric N=1 gauge theories. We focus on branes at orientifolds of the C^3/Z_4, C^3/Z_6 and C^3/Z_6' singularities. We provide a CFT construction of these theories and compute the threshold corrections. Gauge coupling running undergoes two phases: one phase running from the bulk winding scale to the string scale, and a second phase running from the string scale to the infrared. The first phase is associated to the contribution of N=2 sectors to the IR beta functions and the second phase to the contribution of both N=1 and N=2 sectors. In contrast, naive application of the Kaplunovsky-Louis formula gives single running from the bulk winding mode scale. The discrepancy is resolved through 1-loop non-universality of the holomorphic gauge couplings at the singularity, induced by a 1-loop redefinition of the twisted blow-up moduli which couple differently to different gauge nodes. We also study the physics of anomalous and non-anomalous U(1)s and give a CFT description of how masses for non-anomalous U(1)s depend on the global properties of cycles.