Variational methods in supersymmetric lattice field theory: The vacuum sector

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Abstract
The application of variational methods to the computation of the spectrum in supersymmetric lattice theories is considered, with special attention to O(N) supersymmetric σ models. Substantial cancellations are found between bosonic and fermionic contributions even in approximate Ansa$uml—tze for the vacuum wave function. The nonlinear limit of the linear σ model is studied in detail, and it is shown how to construct an appropriate non-Gaussian vacuum wave function for the nonlinear model. The vacuum energy is shown to be of order unity in lattice units in the latter case, after infinite cancellations.