T-branes and Yukawa Couplings

TL;DR

This work investigates T-branes in F-theory GUTs with $Z_{3}$ and $Z_{4}$ monodromies, aimed at breaking $E_{7}$ and $E_{8}$ to $SU(5)_{GUT}$. It employs residue techniques to compute Yukawa couplings for localized matter and analyzes brane recombination via unitary gauge transformations, deriving Toda-like equations for the Higgs field profiles. The key finding is that the $E_{7}$ ($Z_{3}$) breaking yields vanishing up-type and down-type Yukawas, while the $E_{8}$ ($Z_{4}$) breaking produces nonzero Yukawas, including Dirac couplings for right-handed neutrinos, with dimension-four proton decay operators forbidden by extra $U(1)$ symmetries. These results highlight the potential of $E_{8}$-based T-brane constructions to accommodate realistic fermion textures and neutrino masses, while pinpointing open theoretical challenges such as solving the background differential equations and treating RH neutrinos beyond Cartan.

Abstract

We consider various configurations of T-branes which are non-abelian bound states of branes and were recently introduced by Cecotti, Cordova, Heckman and Vafa. They are a refinement of the concept of monodromic branes featured in phenomenological F-theory models. We are particularly interested in the T-branes corresponding to Z3 and Z4 monodromies, which are used to break E7 or E8 gauge groups to SU(5) GUT. Our results imply that the up-type and down-type Yukawa couplings for the breaking of E7 are zero, whereas up-type and down-type Yukawa couplings, together with right handed neutrino Yukawas are non-zero for the case of the breaking of E8. The dimension four proton decay mediating term is avoided in models with either E7 or E8 breaking.