Finite N AdS/CFT Correspondence for Abelian and Nonabelian Orbifolds, and Gauge Coupling Unification

Abstract

Although the AdS/CFT correspondence is rigorous only for an infinite $N \to \infty$ stack of D3-branes, it can be fruitfully studied for finite $N$ as a source of gauge structures and choices for chiral fermions and complex scalars which solve the hierarchy problem by a conformal fixed point. We emphasize orbifolds $AdS_5 \times S^5/\Gamma$ where the resulting GFT has ${\cal N} = 0$ supersymmetry. The fact that the complex scalars are prescribed by the construction limits the possible spontaneous symmetry breaking. Both abelian and nonabelian $\Gamma$ are illustrated by simple examples. An accurate $sin^2 \theta$ in electroweak unification can be obtained, suggesting that this approach merits further study.