Spontaneous Symmetry Breaking and the Renormalization of the Chern-Simons Term

Abstract

We calculate the one-loop perturbative correction to the coefficient of the \cs term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual $U(1)$ symmetry, radiative corrections do not change the coefficient of the \cs term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant \cs term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the \cs term is a discontinuous function over the phase diagram of the theory.

Version to be published in Phys Lett B., minor additional changes

References in corpus (3)

• Chern-Simons Theory as the Large Mass Limit of Topologically Massive Yang-Mills Theory
• On the Coleman-Hill Theorem
• Integer Quantization of the Chern-Simons Coefficient in a Broken Phase

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• Spontaneous gauge symmetry breaking in a supersymmetric Chern-Simons model
• G/G models as the strong coupling limit of topologically massive gauge theory
• Nonminimal planar electrodynamics modified by higher-derivative terms
• The Non-abelian Chern-Simons Coefficient in the Higgs Phase
• Parity Violating Bosonic Loops at Finite Temperature
• Screening Length in 2+1-dimensional Abelian Chern-Simons Theories
• Renormalization In Coupled-Abelian Self-Dual Chern-Simons Models
• The Chern-Simons Coefficient in Supersymmetric Non-abelian Chern-Simons Higgs Theories
• Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories
• Radiative corrections to the Chern-Simons term at finite temperature in the noncommutative Chern-Simons-Higgs model