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Register a new userExact Lattice Supersymmetry at the Quantum Level for N=2 Wess-Zumino models in Lower Dimensions
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Authors
Keisuke Asaka
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We have recently proposed a new lattice SUSY formulation which has exact lattice supersymmetry for Wess-Zumino models in one and two dimensions for all N=2 supercharges. This formulation is non-local in the coordinate space but the difference operator satisfies the Leibniz rule on the newly defined star product. Here we show that this lattice supersymmetry is kept exact at the quantum level by investigating Ward-Takahashi identities up to two loop level.
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Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of $N=2$ lattice Wess-Zumino models in 1- and 2-dimensions. In this approach notorious chiral fermion doublers are treated as physical particles and momentum conservation is modified in such a way that lattice Leibniz rule is satisfied. The two major difficulties to keep exact lattice supersymmetry are overcome. This formulation defines, however, nonlocal field theory. Nevertheless we confirm that exact supersymmetry on the lattice is realized for all supercharges at the quantum level. Delicate issues of associativity are also discussed.
We study dynamical supersymmetry breaking by non perturbative lattice techniques in a class of two-dimensional N=1 Wess-Zumino models. We work in the Hamiltonian formalism and analyze the phase diagram by analytical strong-coupling expansions and explicit numerical simulations with Green Function Monte Carlo methods.
A lattice formulation of the four dimensional Wess-Zumino model that uses Ginsparg-Wilson fermions and keeps exact supersymmetry is presented. The supersymmetry transformation that leaves invariant the action at finite lattice spacing is determined by performing an iterative procedure in the coupling constant. The closure of the algebra, generated by this transformation is also showed.
We consider a lattice formulation of the four dimensional N=1 Wess-Zumino model in terms of the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. The lattice action is invariant under a deformed supersymmetric transformation which is non-linear in the scalar fields and it is determined by an iterative procedure in the coupling constant to all orders in perturbation theory. We also show that the corresponding Ward-Takahashi identity is satisfied at fixed lattice spacing. The calculation is performed in lattice perturbation theory up to order $g^3$ (two-loop) and the Ward-Takahashi identity (containing 110 connected non-tadpole Feynman diagrams) is satisfied at fixed lattice spacing thanks to this exact lattice supersymmetry.
We consider a lattice formulation of the four dimensional N=1 Wess-Zumino model that uses the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. We show that the corresponding Ward-Takahashi identity is satisfied, both at fixed lattice spacing and in the continuum limit. The calculation is performed in lattice perturbation theory up to order $g^2$ in the coupling constant. We also show that this Ward-Takahashi identity determines the finite part of the scalar and fermion renormalization wave functions which automatically leads to restoration of supersymmetry in the continuum limit. In particular, these wave functions coincide in this limit.
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