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

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 $N$.

arXiv comment34 latex pages, 33 figures, 2 tables, anc directory contains txt file with electronic version of the large N critical exponents

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• Five loop renormalization of the Wess-Zumino model
• Instabilities of a Generalized Gross-Neveu Quantum Criticality
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• Spontaneous symmetry breaking of $\mathrm{SO}(2N)$ in Gross--Neveu theory from $2+\epsilon$ expansion