Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 064, 20 pages      arXiv:2102.12767      https://doi.org/10.3842/SIGMA.2021.064
Contribution to the Special Issue on Algebraic Structures in Perturbative Quantum Field Theory in honor of Dirk Kreimer for his 60th birthday

Generalized Gross-Neveu Universality Class with Non-Abelian Symmetry

John A. Gracey
Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, P.O. Box 147, Liverpool, L69 3BX, UK

Received February 26, 2021, in final form June 18, 2021; Published online June 29, 2021

Abstract
We use the large $N$ critical point formalism to compute $d$-dimensional critical exponents at several orders in $1/N$ in an Ising Gross-Neveu universality class where the core interaction includes a Lie group generator. Specifying a particular symmetry group or taking the abelian limit of the final exponents recovers known results but also provides expressions for any Lie group or fermion representation.

Key words: critical exponents; large $N$ expansion; renormalization.

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