The Conformal Sector of F-theory GUTs

Abstract

D3-brane probes of exceptional Yukawa points in F-theory GUTs are natural hidden sectors for particle phenomenology. We find that coupling the probe to the MSSM yields a new class of N = 1 conformal fixed points with computable infrared R-charges. Quite surprisingly, we find that the MSSM only weakly mixes with the strongly coupled sector in the sense that the MSSM fields pick up small exactly computable anomalous dimensions. Additionally, we find that although the states of the probe sector transform as complete GUT multiplets, their coupling to Standard Model fields leads to a calculable threshold correction to the running of the visible sector gauge couplings which improves precision unification. We also briefly consider scenarios in which SUSY is broken in the hidden sector. This leads to a gauge mediated spectrum for the gauginos and first two superpartner generations, with additional contributions to the third generation superpartners and Higgs sector.

Figures (2)

• Figure 1: Depiction (not drawn to scale) of threshold corrections to gauge coupling unification from the D3-brane probe sector (black solid curves). This is to be compared with two-loop MSSM and other contributions with similar effects (red dashed lines). The GUT scale is defined as the scale at which $\alpha_{1}$ and $\alpha_{2}$ unify. The D3-brane threshold correction enters at the scale of conformal symmetry breaking, which is the characteristic mass scale for states of the probe charged under $SU(5)_{GUT}$. Here, we have indicated that the size of the relative shift in couplings $\delta \equiv(\alpha_{3}^{-1}-\alpha_{GUT}^{-1})/\alpha_{GUT}^{-1}$ is positive for two-loop effects and negative for the D3-brane threshold. Balancing these effects improves precision unification.
• Figure 2: Depiction of the various deformations of the D3-brane probe theory. In a limit where gravity is decoupled, in the UV, the D3-brane probes a parallel stack of seven-branes. At a scale $M_{\ast}$, the stack of seven-branes is tilted, inducing a flow to an interacting fixed point, denoted by T-Brane$\oplus D3$. At a scale $M_{GUT}$, a further deformation is added, corresponding to coupling to dynamical Standard Model fields. This leads to a new fixed point, denoted by $SM\oplus$T-Brane$\oplus D3$