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 $N$.

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

References in corpus (1)

• Four-loop critical exponents for the Gross-Neveu-Yukawa models

Cited by in corpus (9)

• Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Twist-tuned quantum criticality in moiré bilayer graphene
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Five loop renormalization of the Wess-Zumino model
• Instabilities of a Generalized Gross-Neveu Quantum Criticality
• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions
• Spontaneous symmetry breaking of $\mathrm{SO}(2N)$ in Gross--Neveu theory from $2+\epsilon$ expansion