Massless excitations at $\theta =\pi$ in the $CP^{N-1}$ model with large values of $N$

TL;DR

This paper reveals a critical transition at  =  in the large N limit of the 2D CP^{N-1} model, showing massless excitations and connections to the quantum Hall effect, challenging previous claims of a persistent mass gap.

Contribution

It establishes a complete critical theory at  =  for the CP^{N-1} model at large N, mapping it onto a 1D Ising model and deriving an effective field theory with exact  functions.

Findings

Diverging correlation length with =1/2

Exact  functions demonstrating quantum Hall features

Massless excitations at  = 

Abstract

We study the instanton vacuum of the $CP^{N-1}$ model with large values of $N$ in 1+1 space-time dimensions. Unlike the longstanding claims which state that the theory always has a mass gap, we for the first time establish a complete {\em critical} theory for the transition at $\theta = \pi$ obtained from a mapping onto the low temperature phase of the 1D Ising model. We derive a simple effective field theory in terms of 1D massless chiral fermions. Our results include, besides a diverging correlation length with an exponent $\nu=1/2$, exact expressions for the $\beta$ functions. These expressions unequivocally demonstrate that the large $N$ expansion with varying $\theta$ displays all the fundamental features of the quantum Hall effect.