GUT Breaking on the Brane

TL;DR

This work presents a five-dimensional supersymmetric SU(5) model where GUT breaking occurs on a brane at scale $M_*$, while matter resides at the brane and gauge/Higgs fields propagate in the bulk. The lightest $X,Y$ gauge bosons and colored Higgs triplets acquire masses tied to the compactification scale $M_C$, and their wavefunctions are repelled from the GUT-breaking brane, significantly suppressing proton decay. Above $M_C$, gauge couplings run log-like rather than power-law, preserving conventional unification with $M_C$ related to the 4D triplet mass, and the model accommodates $O(1)$ Yukawa deviations from SU(5) correlations. The framework also yields testable implications for proton decay (suppressed) and allows larger gauge groups with controlled non-universal running, offering a novel route to GUT phenomenology in extra dimensions.

Abstract

We present a five-dimensional supersymmetric SU(5) theory in which the gauge symmetry is broken maximally (i.e. at the 5D Planck scale M_*) on the same 4D brane where chiral matter is localized. Masses of the lightest Kaluza-Klein modes for the colored Higgs and X and Y gauge fields are determined by the compactification scale of the fifth dimension, M_C ~ 10^{15} GeV, rather than by M_*. These fields' wave functions are repelled from the GUT-breaking brane, so that proton decay rates are suppressed below experimental limits. Above the compactification scale, the differences between the standard model gauge couplings evolve logarithmically, so that ordinary logarithmic gauge coupling unification is preserved. The maximal breaking of the grand unified group can also lead to other effects, such as O(1) deviations from SU(5) predictions of Yukawa couplings, even in models utilizing the Froggatt-Nielsen mechanism.

Figures (3)

• Figure 1: Mass spectrum for the lowest KK modes of the gauge fields (a), and Higgs fields (b) in our model. As explained in the text, the transition to degeneracy between the $X,Y$ and 3-2-1 towers occurs much more gradually than shown in (a). In (b), the limit of very large $\kappa$ is taken, so that the slight non-degeneracy between the colored hypermultiplet pairs at each level is not resolved. In both (a) and (b), the triplet of numbers below each tower corresponds to the beta function contribution $(b_1,b_2,b_3)$ that comes from each level in that tower (for the colored Higgs, the contributions from the nearly-degenerate hypermultiplet pairs are combined).
• Figure 2: The qualitative picture for gauge coupling unification in our 5D model. We define $\delta_i(\mu) \equiv \alpha^{-1}_i(\mu)-\alpha^{-1}_1(\mu)$. The conventional unification scale $M_{\rm GUT}\sim 2 \times 10^{16}$ GeV is a derived scale rather than a physical one. Here we assume $m_{\Sigma}<g_5^2 \langle \Sigma \rangle^2$, so that unification is achieved near $g_5^2 \langle \Sigma \rangle^2$.
• Figure 3: Values of $M_{\Sigma}$ and $g_{5}^2 \langle \Sigma \rangle^2$ which generate the same threshold effect above $M_{C}$ as is generated in minimal supersymmetric SU(5) between $M_{H_{C}}$ and $M_{\rm GUT}$. The dashed line corresponds to $M_{C}=6\times 10^{14}~{\rm GeV}$, while the solid line corresponds to $M_{C}=6\times 10^{15}~{\rm GeV}$. To calculate these lines we have used first-order solutions in $(g_{5}^{2} \langle \Sigma \rangle^{2} R)^{-1}$ for the $X$ and $Y$ masses.