On the O(1/N^2) Beta-Function of the Nambu-Jona-Lasinio Model with Non-Abelian Chiral Symmetry

Abstract

We present the formalism for computing the critical exponent corresponding to the $\beta$-function of the Nambu--Jona-Lasinio model with $SU(M)$ $\times$ $SU(M)$ continuous chiral symmetry at $O(1/N^2)$ in a large $N$ expansion, where $N$ is the number of fermions. We find that the equations can only be solved for the case $M$ $=$ $2$ and subsequently an analytic expression is then derived. This contrasting behaviour between the $M$ $=$ $2$ and $M$ $>$ $2$ cases, which appears first at $O(1/N^2)$, is related to the fact that the anomalous dimensions of the bosonic fields are only equivalent for $M$ $=$ $2$.

23 pages, 4 figures (available from author on request), in latex, LTH-314

References in corpus (7)

• Four - Fermi Theories in Fewer Than Four Dimensions
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• The Nambu-Jona-Lasinio Model at O(1/N^2)
• On Calculation of 1/n Expansions of Critical Exponents in the Gross-Neveu Model with the Conformal Technique
• The Beta-Function of the Chiral Gross Neveu Model at O(1/N^2)
• Algorithm for Computing the $\BETA$-Function of Quantum Electrodynamics in the Large N_f Expansion
• Gauge Independent Critical Exponents for QED Coupled to a Four Fermi Interaction with and without a Chern Simons Term

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