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

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

1993-07-26

arxiv.org/abs/hep-th/9307156v1

Z. Phys. C61 (1994) 115-124

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/BF01641894

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 $M$ $=$ $2$.

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