ar X iv : h ep - t h / 94 11 12 4 v 2 1 7 N ov 1 99 4 Mass Degeneracies In Self - Dual Models ∗

An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs systems leads to coupled abelian models with interesting mass spectra. The vacua are characterized by embeddings of SU(2) into the gauge algebra, and in the broken phases the gauge and real scalar masses coincide, reflecting the relation of these self-dual models to N = 2 SUSY. The masses themselves are related to the exponents of the gauge algebra, and the self-duality equation is a deformation of the classical Toda equations. The self-dual Chern-Simons systems [1, 2, 3, 4] may be characterized by the fact that the energy density possesses a Bogomol’nyi lower bound which is saturated by solutions to first-order self-duality equations. The special form of the self-dual potential may also be fixed by embedding this bosonic system into a supersymmetric model and imposing the condition of N = 2 SUSY [5]. Each of these characterizations is familiar from other self-dual systems [6, 7]. In this Letter we investigate another characterization of self-dual models, in terms of the spectra of massive excitations in the various vacua, when the model is viewed as a spontaneous symmetry breaking system. This is of particular interest for ChernSimons systems because the Higgs mechanism works in an unfamiliar manner [8]. We find that in self-dual Chern-Simons theories associated with the simply-laced A-D-E Lie algebras ∗UCONN-94-9; hep-th/9411124 1 the gauge and real scalar mass spectra are degenerate in each of the (many) inequivalent vacua. Furthermore, the masses are given by a simple universal mass formula in terms of the exponents of the algebra. The nonabelian relativistic self-dual Chern-Simons system [1, 2, 3, 4] is described by the following Lagrange density (in 2 + 1 dimensional spacetime) L = −tr ( (Dμφ) Dφ )