Towards exact field theory results for the Standard Model on fractional D6-branes

TL;DR

This paper develops a method to derive exact low-energy effective actions for the Standard Model realized on fractional D6-branes in orbifold backgrounds, extending previous approaches from toroidal to orbifold settings.

Contribution

It generalizes the matching of string theoretic gauge couplings to supergravity from toroidal to orbifold backgrounds, enabling classification of Kaehler metrics and gauge kinetic functions.

Findings

Classification of Kaehler metrics and gauge kinetic functions based on intersection angles.

Potential to extend results to smooth Calabi-Yau backgrounds.

Provides a framework for exact field theory results in string compactifications.

Abstract

Fractional D6-branes on toroidal orbifold backgrounds are known to be able to accommodate the particle spectrum and gauge group of the Standard Model, but up to now exact results for their low-energy effective action are missing. Here we discuss how the conceptual ansatz of matching the string theoretic gauge couplings at one-loop with the supergravity expressions is generalised from the six-torus to orbifold backgrounds on which the Standard Model spectrum can be realised on fractional D6-branes. The Kaehler metrics and perturbatively exact holomorphic gauge kinetic functions can be classified in terms of the vanishing of some intersection angle and the related beta function coefficients, which potentially opens the possibility to extrapolate to smooth Calabi-Yau backgrounds.