Critical exponent $\eta$ at $O(1/N^3)$ in the chiral XY model using the large $N$ conformal bootstrap

TL;DR

This paper calculates the third-order correction to the critical exponent η in the chiral XY model using large N conformal bootstrap techniques, providing more accurate estimates in three dimensions.

Contribution

It introduces a novel approach by applying the large N conformal bootstrap to compute higher-order corrections in the chiral XY model.

Findings

Computed $O(1/N^3)$ correction to η in the chiral XY model.

Provided improved estimates of η for various N in 3D.

Linked the Nambu-Jona-Lasinio model to the chiral XY model results.

Abstract

We compute the $O(1/N^3)$ correction to the critical exponent $\eta$ in the chiral XY or chiral Gross-Neveu model in $d$-dimensions. As the leading order vertex anomalous dimension vanishes, the direct application of the large $N$ conformal bootstrap formalism is not immediately possible. To circumvent this we consider the more general Nambu-Jona-Lasinio model for a general non-abelian Lie group. Taking the abelian limit of the exponents of this model produces those of the chiral XY model. Subsequently we provide improved estimates for $\eta$ in the three dimensional chiral XY model for various values of $N$.