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On Gauge Threshold Corrections for Local IIB/F-theory GUTs

Joseph P. Conlon, Eran Palti

TL;DR

The paper analyzes gauge threshold corrections in local IIB/F-theory GUTs with hypercharge flux breaking, showing that holomorphy and the Kaplunovsky-Louis formula shift the unification scale to the winding scale $M_X = R M_s$. Field-theory arguments tie this to the structure of holomorphic gauge kinetic functions and bulk-volume effects, while a string-theory perspective using open-closed string duality explains the winding-scale cutoff via globally trivial hypercharge flux inducing a bulk-propagating RR sector. The results extend beyond orbifold limits and apply to warped-throat geometries, where the cutoff can approach the Planck scale, with possible implications for TeV-scale strings in certain setups and for LARGE volume scenario phenomenology. Overall, the work emphasizes that bulk geometry cannot be fully decoupled in local GUT constructions and that the unification scale is intimately linked to the bulk radius through the winding scale.

Abstract

We study gauge threshold corrections for local GUT models in IIB/F-theory. Consistency with holomorphy requirements of supergravity and the Kaplunovsky-Louis formula implies that the unification scale is enhanced by the bulk radius R from the string scale to M_X =RM_S. We argue that the stringy interpretation of this is via a locally uncancelled tadpole sourced by the hypercharge flux. This sources closed string modes propagating into the bulk; equivalently open string gauge coupling running up to the winding scale M_X. The enhancement to R M_s is tied to GUT breaking by a globally trivial hypercharge flux and will occur in all models realising this mechanism.

On Gauge Threshold Corrections for Local IIB/F-theory GUTs

TL;DR

The paper analyzes gauge threshold corrections in local IIB/F-theory GUTs with hypercharge flux breaking, showing that holomorphy and the Kaplunovsky-Louis formula shift the unification scale to the winding scale . Field-theory arguments tie this to the structure of holomorphic gauge kinetic functions and bulk-volume effects, while a string-theory perspective using open-closed string duality explains the winding-scale cutoff via globally trivial hypercharge flux inducing a bulk-propagating RR sector. The results extend beyond orbifold limits and apply to warped-throat geometries, where the cutoff can approach the Planck scale, with possible implications for TeV-scale strings in certain setups and for LARGE volume scenario phenomenology. Overall, the work emphasizes that bulk geometry cannot be fully decoupled in local GUT constructions and that the unification scale is intimately linked to the bulk radius through the winding scale.

Abstract

We study gauge threshold corrections for local GUT models in IIB/F-theory. Consistency with holomorphy requirements of supergravity and the Kaplunovsky-Louis formula implies that the unification scale is enhanced by the bulk radius R from the string scale to M_X =RM_S. We argue that the stringy interpretation of this is via a locally uncancelled tadpole sourced by the hypercharge flux. This sources closed string modes propagating into the bulk; equivalently open string gauge coupling running up to the winding scale M_X. The enhancement to R M_s is tied to GUT breaking by a globally trivial hypercharge flux and will occur in all models realising this mechanism.

Paper Structure

This paper contains 5 sections, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Local GUTs and field theory
  3. The string picture
  4. GUTs and warped throats
  5. Conclusions

Figures (2)

  • Figure 1: The locally divergent string diagram in the presence of hypercharge flux breaking. The diagram consists of a 1-loop open string diagram in the presence of a background spacetime gauge field (or equivalently with the insertion of two gauge vertex operators). The ultraviolet limit of this diagram is the infrared limit of the closed string tree-diagram, which diverges due to the intermediate massless propagator.
  • Figure 2: The schematic geometry. The hypercharged flux is on a cycle that is nontrivial locally and trivial globally.