The U(1)s in the Finite N Limit of Orbifold Field Theories

Abstract

We study theories generated by orbifolding the {\cal N}=4 super conformal U(N) Yang Mills theory with finite N, focusing on the rôle of the remnant U(1) gauge symmetries of the orbifold process. It is well known that the one loop beta functions of the non abelian SU(N) gauge couplings vanish in these theories. It is also known that in the large N limit the beta functions vanish to all order in perturbation theory. We show that the beta functions of the non abelian SU(N) gauge couplings vanish to two and three loop order even for finite N. This is the result of taking the abelian U(1) of U(N)=SU(N)xU(1) into account. However, the abelian U(1) gauge couplings have a non vanishing beta function. Hence, those theories are not conformal for finite N. We analyze the renormalization group flow of the orbifold theories, discuss the suppression of the cosmological constant and tackle the hierarchy problem in the non supersymmetric models.

2+35 pages, 2 figures, LaTex

References in corpus (5)

• Large N Field Theories, String Theory and Gravity
• Magnetic fields, branes and noncommutative geometry
• Dualities of Type 0 Strings
• Beta Functions of Orbifold Theories and the Hierarchy Problem
• Conformal Approach to Particle Phenomenology

Cited by in corpus (6)

• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• Perturbative Search for Fixed Lines in Large N Gauge Theories
• Perturbative Gauge Theory and Closed String Tachyons
• N = 2 Gauge/Gravity Duals
• Conformal Completion of the Standard Model with a Fourth Generation
• Chiral Fermions and Quadratic Divergences