Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis

Abstract

A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\le N\le 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass-gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge invariant variables is also presented.

31 pages, References added, typos corrected

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• The Yang-Mills vacuum wave functional in three dimensions at weak coupling
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• On the Gauge-invariant Functional Measure for Gauge Fields on CP^2
• Holographic k-string Tensions in Higher Representations and Luescher Term Universality
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• 3d N=4 Super-Yang-Mills on a Lattice
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• Fermions, Mass-Gap and Landau Levels: Gauge invariant Hamiltonian for QCD in D=2+1
• The Yang-Mills Vacuum Wave Functional in 2+1 Dimensions
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