11 are grateful to H. Gies for useful comments on the manuscript. FS acknowledges support by the Studien- stiftung des deutschen Volkes. This work has been sup- ported by the DFG-Research Training Group ”Quantum- and Gravitational Fields” GRK 1523/1. we find that supersymmetry breaking is governed by the relevant direction. The finite-temperature flow equations are obtained by replacing the integration over the time-like direction by a sum over Matsubara frequencies. As bosons and fermions obey different thermal boundary conditions, finite tem- peratures introduce a soft supersymmetry breaking. In the phase with broken supersymmetry (restored GLYPH<CI> 2 symmetry) at zero temperature the three-dimensional Wess-Zumino model flows to a massless field theory. In the GLYPH<CI> 2 symmetric phase at finite temperature the model therefore behaves like a three-dimensional gas of massless bosons. We have found that this is indeed the case. The small deviations from the ideal-gas law found in our nu- merical studies originate from the self-interaction of the bosons. In this Addendum we derive the Wetterich flow equa- tion in Minkowski space. For the sake of simplicity we consider a real scalar field in this appendix. The gener- alization to other fields, such as fermion or gauge fields, is straightforward. The generating functional in Minkowski-space is given by where J denotes the external source and ( J, ϕ ) ≡ ∫ d $^{d}$x J ( x ) ϕ ( x ). The generating functional W for the connected two-point functions, the so-called Schwinger functional, reads 12 From this we obtain The effective action is the Legendre transform of the Schwinger functional, where φ is the mean (classical) field. Using δ $_{δJ}$W [ J ] = − φ , we obtain the equation of motion for the field φ : The scale-dependent generating functional is defined as with Helpful discussions with H. Gies and J. M. Pawlowski are gratefully acknowledged. Moreover the authors Throughout this paper we have addressed several sim- ilarities and differences between scalar O ( N ) models and the N = 1 Wess-Zumino model at zero and finite temper- atures, e. g. the fixed-point structure at zero temperature and the behavior at finite temperature. A detailed ex- ploration of both models with respect to their similarities and differences, in particular with respect to the large- N limit, is deferred to future work. Even though supersymmetry is explicitly broken at fi- nite temperature, the GLYPH<CI> 2 symmetry of the model can be either restored or broken at finite temperature. Whether GLYPH<CI> 2 symmetry is broken or not depends on the tempera- ture (and parameters of the model, i. e. the initial values of the couplings at the initial RG scale). Since supersym- metry and GLYPH<CI> 2 symmetry are intimately linked we have argued that a study of GLYPH<CI> 2 symmetry may be used to measure the strength of supersymmetry breaking. We have computed the phase diagram for the restoration of Z$_{2}$ symmetry at finite temperatures. We find two dif- ferent types of phases which are separated by a second order phase transition: one phase with soft supersym- metry breaking due to finite temperature but broken GLYPH<CI> 2 symmetry and one with restored GLYPH<CI> 2 symmetry. At high temperatures, supersymmetry breaking mani- fests itself in the fact that the flow equations for the su- perpotential, derived from the bosonic and the fermionic part of the action, are different. We also observe dimen- sional reduction in the way that, after a suitable rescal- ing, the flow equation for the ”bosonic” superpotential in three dimensions reduces to the flow equation in two dimensions. Due to the absence of a fermionic thermal zero-mode the fermions do not contribute to the RG flow for small scales k ≪ T . We have argued that the radius of convergence for the polynomial expansion of the super- field interpolates between the values for two and three dimensions as the temperature is raised. Appendix A: Derivation of the flow equations in Minkowski space Z [ J ] = ∫ D ϕ e i ( S [ ϕ ]+( J,ϕ $^{))}$, W [ J ] = i ln Z [ j ] . δ δJ W [ J ] = i δ δJ ln Z [ J ] = − ∫ D φ e i ( S + ∫ Jφ $^{)}$φ φ e i ( S +( J,ϕ )) = − φ = −〈 ϕ 〉 . Γ[ φ ] = − W [ J ] − ( J, φ ) , δ Γ[ φ ] δφ = − ∫ d $^{d}$y δW [ J ] δJ ( y ) δJ ( y ) δφ ( x ) − ∫ d $^{d}$y δJ ( y ) δφ ( x ) φ ( y ) − J ( x ) = − J ( x ) . Z$_{k}$ [ J ] = e − iW k [ J ] = e i Δ S k [ δ $^{$_{δJ}$]}$Z [ J ] = ∫ D ϕ e i ( S [ ϕ ]+ ∫$_{x}$ ϕJ +Δ S k [ ϕ ]) Δ S$_{k}$ [ φ ] = 1 2 ∫ d $^{4}$q (2 π ) $_{4}$ϕ ( − q ) R$_{k}$ ( q ) ϕ ( q ) . ACKNOWLEDGMENTS 12 The generating functional W of connected two-point functions should not be confused with the super potential in the main part.