Grand Unification and Enhanced Quantum Gravitational Effects

In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if higher dimensional operators induced by gravity are taken into consideration. We show that the generic size of, and the uncertainty in, these effects from gravity can be larger than the two-loop corrections typically considered in renormalization group analyses of unification. In some cases, gravitational effects of modest size can render unification impossible.

Figure 1

For $\eta$ fixed by the particle content of the theory, solid lines are contours of constant $c$ such that, under the presence of the gravitationally induced and enhanced operator (5), SUSY-SU(5) perfectly unifies at two loops for given values of the initial strong coupling constant ${\alpha }_3(M_Z)$ and SUSY breaking scale $M_{\mathrm{SUSY}}$. Over the whole range, unification happens for some value of the coefficient $c$, with unification scale and unified coupling between $M_X=9.3\times {10}^{14}\mathrm{GeV}$, ${\alpha }_G=0.033$ (lower right corner) and $M_X=5.5\times {10}^{16}\mathrm{GeV}$, ${\alpha }_G=0.045$ (upper left).