Critical exponent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> in the chiral XY model using the large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> conformal bootstrap

Abstract

We compute the $O(1/{N}^{3})$ correction to the critical exponent $\ensuremath{\eta}$ 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 $\ensuremath{\eta}$ in the three-dimensional chiral XY model for various values of $N$.

Topics & Concepts