F-theory Yukawa Couplings and Supersymmetric Quantum Mechanics

TL;DR

This paper explores how supersymmetric quantum mechanics algebra governs fermion localization on D7-brane intersections in F-theory, influencing proton decay operators and neutrino masses, with implications for string phenomenology.

Contribution

It reveals the role of N=2 supersymmetric quantum mechanics algebra in constraining physical operators and studies the effects of fluxes and metric perturbations on localized solutions.

Findings

Certain proton decay operators are forbidden by the algebra

Majorana neutrino mass term is allowed in the model

Localized solutions are affected by fluxes and metric perturbations

Abstract

The localized fermions on the intersection curve $\Sigma$ of D7-branes, are connected to a N=2 supersymmetric quantum mechanics algebra. Due to this algebra the fields obey a global U(1) symmetry. This symmetry restricts the proton decay operators and the neutrino mass terms. Particularly, we find that several proton decay operators are forbidden and the Majorana mass term is the only one allowed in the theory. A special SUSY QM algebra is studied at the end of the paper. In addition we study the impact of a non-trivial holomorphic metric perturbation on the localized solutions along each matter curve. Moreover, we study the connection of the localized solutions to an N=2 supersymmetric quantum mechanics algebra when background fluxes are turned on.