Gauge Threshold Corrections for Local String Models

TL;DR

This paper analyzes gauge threshold corrections in local string models embedded in large compact spaces, showing that the Kaplunovsky–Louis framework implies a unification scale shift from the string scale $M_s$ to $M_X = R M_s$, with $R=(M_P/M_s)^{1/3}$. It validates this result via explicit string computations for D3/D3 models at orbifold singularities, where twisted RR tadpoles and the large-volume Kähler potential drive the running, and discusses D3/D7 models where backreaction complicates the locality assumption. The calculations use the background-field method across unmagnetised and magnetised sectors, revealing that only $\mathcal{N}=2$ sectors contribute to gauge running in local models, with $\mathcal{N}=1$ sectors canceling due to local tadpole constraints. The UV divergences in the local theory reflect uncancelled bulk tadpoles, which in a global embedding are cured by states with mass $M_X$, effectively cutting off the running at $M_X$. The findings imply that local models with intermediate string scales can still achieve gauge coupling unification, though the precise details depend on the global geometry and potential backreaction effects, with significant phenomenological implications for GUT-scale physics and proton decay.

Abstract

We study gauge threshold corrections for local brane models embedded in a large compact space. A large bulk volume gives important contributions to the Konishi and super-Weyl anomalies and the effective field theory analysis implies the unification scale should be enhanced in a model-independent way from M_s to R M_s. For local D3/D3 models this result is supported by the explicit string computations. In this case the scale R M_s comes from the necessity of global cancellation of RR tadpoles sourced by the local model. We also study D3/D7 models and discuss discrepancies with the effective field theory analysis. We comment on phenomenological implications for gauge coupling unification and for the GUT scale.

Figures (7)

• Figure 1: The quiver for the $\mathbb{Z}_4$ singularity.
• Figure 2: The $T^6/\mathbb{Z}_4$ orbifold. Dark circles correspond to $\theta^1$ fixed points and hollow squares correspond to $\theta^2$ fixed points.
• Figure 3: The quiver for the $\mathbb{Z}_6$ singularity.
• Figure 4: The quiver for the $\mathbb{Z}_6'$ singularity.
• Figure 5: The quiver for the $\Delta_{27}$ singularity.