Two-loop analysis of non-Abelian Chern-Simons theory

Journal Article · Tue Dec 15 04:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.5521· OSTI ID:7158938

Chen, W ^[1]; Semenoff, G W ^[2]; Wu, Y ^[3]

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1. Department of Physics, University of Utah, Salt Lake City, Utah 84112 (United States) Department of Physics, University of British Columbia, Vancouver, British Columbia, V6T 1Z1 (Canada)
2. Department of Physics, University of British Columbia, Vancouver, British Columbia, V6T 1Z1 (Canada)
3. Department of Physics, University of Utah, Salt Lake City, Utah 84112 (United States)

Perturbative renormalization of a non-Abelian Chern-Simons gauge theory is examined. It is demonstrated by explicit calculation that, in the pure Chern-Simons theory, the [beta] function for the coefficient of the Chern-Simons term vanishes to three-loop order. Both dimensional regularization and regularization by introducing a conventional Yang-Mills 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 Slavnov-Taylor identity to two loops and gives no renormalization of the Chern-Simons term. Regularization with the Yang-Mills term yields a finite integer-valued renormalization of the coefficient of the Chern-Simons term at one loop, and we conjecture no renormalization at higher order. We also examine the renormalization of Chern-Simons theory coupled to matter. We show that in the non-Abelian case the Chern-Simons gauge field as well as the matter fields require infinite renormalization at two loops and therefore obtain nontrivial anomalous dimensions. We show that the [beta] function for the gauge coupling constant is zero to two-loop order, consistent with the topological quantization condition for this constant.

• OSTI ID: 7158938
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 46:12; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
CORRELATION FUNCTIONS
COUPLING CONSTANTS
EUCLIDEAN SPACE
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
MATHEMATICAL SPACE
MATHEMATICS
PARTITION FUNCTIONS
PERTURBATION THEORY
QUANTIZATION
QUANTUM FIELD THEORY
RENORMALIZATION
RIEMANN SPACE
SPACE
SPACE-TIME
SUPERSYMMETRY
SYMMETRY
TOPOLOGY
WILSON LOOP
YANG-MILLS THEORY