An Exceptional Sector for F-theory GUTs

TL;DR

This paper investigates D3-brane probes at exceptional E-type Yukawa points in local F-theory GUTs. It shows that such probes realize an $\,\mathcal{N}=2\$ SCFT (Minahan–Nemeschansky) decoupled from a free hypermultiplet, which is deformed to an $\,\mathcal{N}=1\$ theory by seven-brane monodromy and flux, coupling to the Standard Model via F-terms and matter-wave profiles. The authors analyze how the probe affects SM gauge coupling running, possible kinetic mixing with a hidden $U(1)$, and the conditions under which the visible sector remains perturbatively unified; they argue trivial monodromy flows back to the original theory, while nontrivial monodromy may yield an interacting IR CFT. They also discuss phenomenological implications, including potential roles in SUSY breaking, gauge mediation, and inflation, and suggest directions for further study, such as holographic descriptions and more detailed monodromy analyses.

Abstract

D3-branes are often a necessary ingredient in global compactifications of F-theory. In minimal realizations of flavor hierarchies in F-theory GUT models, suitable fluxes are turned on, which in turn attract D3-branes to the Yukawa points. Of particular importance are ``E-type'' Yukawa points, as they are required to realize a large top quark mass. In this paper we study the worldvolume theory of a D3-brane probing such an E-point. D3-brane probes of isolated exceptional singularities lead to strongly coupled N = 2 CFTs of the type found by Minahan and Nemeschansky. We show that the local data of an E-point probe theory determines an N = 1 deformation of the original N = 2 theory which couples this strongly interacting CFT to a free hypermultiplet. Monodromy in the seven-brane configuration translates to a novel class of deformations of the CFT. We study how the probe theory couples to the Standard Model, determining the most relevant F-term couplings, the effect of the probe on the running of the Standard Model gauge couplings, as well as possible sources of kinetic mixing with the Standard Model.

Figures (1)

• Figure 1: Depiction of a D3-brane probe of a seven-brane with $E_{6}$ gauge group. In the configuration on the left, we have the Minahan-Nemeschansky $\mathcal{N}=2$ theory with $E_{6}$ flavor symmetry and a decoupled $\mathcal{N}=2$ hypermultiplet. A Yukawa point is locally described by tilting the seven-branes so that they still enhance to $E_{6}$ at the point probed by the D3-brane. In the probe theory this corresponds to an $\mathcal{N}=1$ deformation which couples the Minahan Nemeschansky theory and free hypermultiplet.