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

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We revisit the θ dependence in CPⁿ⁻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 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.