Twoloop analysis of nonAbelian ChernSimons theory
Abstract
Perturbative renormalization of a nonAbelian ChernSimons gauge theory is examined. It is demonstrated by explicit calculation that, in the pure ChernSimons theory, the β function for the coefficient of the ChernSimons term vanishes to threeloop order. Both dimensional regularization and regularization by introducing a conventional YangMills term in the action are used. It is shown that dimensional regularization is not gauge invariant at two loops. A variant of this procedure, similar to regularization by dimensional reduction used in supersymmetric field theories, is shown to obey the SlavnovTaylor identity to two loops and gives no renormalization of the ChernSimons term. Regularization with the YangMills term yields a finite integervalued renormalization of the coefficient of the ChernSimons term at one loop, and we conjecture no renormalization at higher order. We also examine the renormalization of ChernSimons theory coupled to matter. We show that in the nonAbelian case the ChernSimons gauge field as well as the matter fields require infinite renormalization at two loops and therefore obtain nontrivial anomalous dimensions. We show that the β function for the gauge coupling constant is zero to twoloop order, consistent with the topological quantization condition for this constant.
 Publication:

Physical Review D
 Pub Date:
 December 1992
 DOI:
 10.1103/PhysRevD.46.5521
 arXiv:
 arXiv:hepth/9209005
 Bibcode:
 1992PhRvD..46.5521C
 Keywords:

 11.10.Gh;
 03.70.+k;
 11.15.Bt;
 Renormalization;
 Theory of quantized fields;
 General properties of perturbation theory;
 High Energy Physics  Theory
 EPrint:
 48 pages, UU/HEP/91/12