Conformality and Unification of Gauge Couplings

Conformality is inspired by superstring duality and assumes that the particle spectrum of the standard model is enriched such that there is a conformal fixed point of the renormalization group at the TeV scale. Above this scale the coupling do not run so the hierarchy is nullified. Until very recently, the possibility of testing string theory seemed at best remote. The advent of AdS/CFT s and large-scale string compactification suggest this point of view may be too pessimistic, since both could lead to ∼ 100TeV evidence for strings. With this thought in mind, we are encouraged to build AdS/CFT models with realistic fermionic structure, and reduce to the standard model below ∼ 1TeV . Using AdS/CFT duality, one arrives at a class of gauge field theories of special recent interest. The simplest compactification of a ten-dimensional superstring on a product of an AdS space with a five-dimensional spherical manifold leads to an N=4 SU(N) supersymmetric gauge theory, well known to be conformally invariant. By replacing the manifold S by an orbifold S/Γ one arrives at less supersymmetries corresponding to N = 2, 1 or 0 depending 2 on whether Γ ⊂ SU(2), SU(3), or 6 ⊂SU(3) respectively, where Γ is in all cases a subgroup of SU(4) ∼ SO(6) the isometry of the S manifold. It was conjectured in 3 that such SU(N) gauge theories are conformal