The large N theory exactly reveals the quantum Hall effect and theta-renormalization

Abstract

We revisit the $θ$ dependence in $CP^{N-1}$ model with large $N$. We study the consequences of a recently discovered new ingredient of the instanton vacuum, i.e. the massless chiral edge excitations. Contrary to the previous believes, our results demonstrate that the large $N$ expansion displays all the fundamental features of the quantum Hall effect. This includes the {\em robust} quantization of the Hall conductance, as well as the appearance of massless bulk excitations at $θ= π$. We conclude that the quantum Hall effect is a generic feature of the instanton vacuum, i.e. for any number of field components and not just for the theory in the replica limit alone.