Abstract
We confirm the convergence of the derivative expansion in two supersymmetric models via the functional renormalization group method. Using pseudo-spectral methods, high-accuracy results for the lowest energies in supersymmetric quantum mechanics and a detailed description of the supersymmetric analogue of the Wilson-Fisher fixed point of the three-dimensional Wess-Zumino model are obtained. The superscaling relation proposed earlier, relating the relevant critical exponent to the anomalous dimension, is shown to be valid to all orders in the supercovariant derivative expansion and for all $d \ge 2$.
Highlights
A well-established method to study non-perturbative effects in supersymmetric theories is based on a discretization of spacetime and the corresponding supersymmetric lattice models, see e.g. [1,2,3,4,5,6,7,8]
The paper is organized as follows: in section 2 we review the relevant features of SUSY quantum mechanics
We obtain the flow equations in Euclidean space with metric −δμν via a Wick rotation of the zeroth momentum component, i.e. q0 → iq0. These equations are by construction identically to the ones derived in SUSY quantum mechanics up to an integration over a three dimensional momentum space
Summary
In order to derive the flow equations for supersymmetric quantum mechanics, we employ the superfield formalism [29]. The Euclidean superfield, expanded in terms of the anticommuting Grassmann variables θ and θ, reads. In order to obtain a supersymmetric action, we further need the supercovariant derivatives D = i∂θ − θ∂τ and D = i∂θ − θ∂τ They fulfill almost identical anticommutation relations as the supercharges,. With these definitions, one can write down the supersymmetric Euclidean off-shell action within the superfield formalism: S[φ, F, ψ, ψ] =. The effective potential exhibits a ground state with positive energy and supersymmetry is spontaneously broken, even if we may start with a microscopic potential with vanishing ground state energy This applies e.g. to cubic classical superpotentials of the form.
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