Quiver Gauge Theory and Unification at About 4 Tev

Abstract

The use of the AdS/CFT correspondence to arrive at quiver gauge field theories is dicussed, focusing on the orbifolded case without supersymmetry. An abelian orbifold with the finite group Zp can give rise to a G = SU (N ) p gauge group with chiral fermions and complex scalars in different bi-fundamental representations of G. The precision measurements at the Z resonance suggest the values p = 12 and N = 3, and a unifications scale M U ∼ 4 TeV.The robustness and predictivity of such grand unification is discussed. Quiver Gauge TheoryThe relationship of the Type IIB superstring to conformal gauge theory in d = 4 gives rise to an interesting class of gauge theories. Choosing the simplest compactification 1 on AdS 5 × S 5 gives rise to an N = 4 SU(N) gauge theory which is known to be conformal due to the extended global supersymmetry and non-renormalization theorems. All of the RGE β−functions for this N = 4 case are vanishing in perturbation theory. It is possible to break the N = 4 to N = 2, 1, 0 by replacing S 5 by an orbifold S 5 /Γ where Γ is a discrete group with Γ ⊂ SU (2), ⊂ SU (3), ⊂ SU (3) respectively.In building a conformal gauge theory model 2,3,4 , the steps are: (1) Choose the discrete group Γ; (2) Embed Γ ⊂ SU (4); (3) Choose the N of SU (N ); and (4) Embed the Standard Model SU (3) × SU (2) × U (1) in the resultant gauge group SU (N ) p (quiver node identification). Here we shall look only at abelian Γ = Z p and define α = exp(2πi/p). It is expected from the string-field duality that the resultant field theory is conformal in the N −→ ∞ limit, and will have a fixed manifold, or at least a fixed point, for N finite.Before focusing on N = 0 non-supersymmetric cases, let us first examine an N = 1 model first put forward in the work of Kachru and Silverstein 5 .