arXiv subjects

Georg Bergner

Publications and source records attributed to Georg Bergner.

95 records · Page 6Linked to original sources

arXiv2008

Generalisations of the Ginsparg-Wilson relation and a remnant of supersymmetry on the lattice

We introduce a lattice symmetry relation for field theories with general linear symmetries. For chiral symmetry the well-known Ginsparg-Wilson relation is reproduced. The new relation encodes the remnant of the original symmetry on the lattice and guides the construction of invariant lattice actions. We apply this approach to lattice supersymmetry. There, an additional constraint has to be satisfied which originates in the derivative operator in the symmetry transformations. As a consequence the non-local SLAC derivative operator appears in the lattice transformation. Despite this non-local form we show how local solutions for quadratic actions can be found. For interacting theories the relation in general leads to a non-polynomial action that can be reduced to a finite polynomial order only under certain conditions.

hep-lat↗

arXiv2008

Numerical Investigation of the 2D N=2 Wess-Zumino Model

We study lattice formulations of the two-dimensional N=2 Wess-Zumino model with a cubic superpotential. Discretizations with and without lattice supersymmetries are compared. We observe that the "Nicolai improvement" introduces new problems to simulations of the supersymmetric model. With high statistics we check the degeneracy of bosonic and fermionic masses on the lattice. Perturbative mass corrections to one-loop order are compared with continuum extrapolations of our lattice results in the weakly coupled regime. For intermediate couplings first results of fermionic masses in the continuum are presented where deviations from the perturbative result are observed.

hep-lat↗

arXiv2008

Two-Dimensional Wess-Zumino Models at Intermediate Couplings

We consider the two-dimensional N=(2,2) Wess-Zumino model with a cubic superpotential at weak and intermediate couplings. Refined algorithms allow for the extraction of reliable masses in a region where perturbation theory no longer applies. We scrutinize the Nicolai improvement program which is supposed to guarantee lattice supersymmetry and compare the results for ordinary and non-standard Wilson fermions with those for SLAC derivatives. It turns out that this improvement completely fails to enhance simulations for Wilson fermions and only leads to better results for SLAC fermions. Furthermore, even without improvement terms the models with all three fermion species reproduce the correct values for the fermion masses in the continuum limit.

hep-lat↗

arXiv2007

Supersymmetric lattice models in one and two dimensions

We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to discretizations of surface integrals. In particular, we check that fermionic and bosonic masses coincide and the unbroken Ward identities are fulfilled to high accuracy. Equally good results for the effective masses can be obtained in a model with the SLAC derivative (even without improvement terms). In two dimensions we introduce a non-standard Wilson term in such a way that the discretization errors of the kinetic terms are only of order a squared. Masses extracted from the corresponding manifestly supersymmetric model prove to approach their continuum values much quicker than those from a model containing the standard Wilson term. Again, a comparable enhancement can be achieved in a theory using the SLAC derivative.

hep-lat↗

arXiv2007

Low-dimensional Supersymmetric Lattice Models

We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to discretizations of surface integrals. In one dimension, our simulations show that a model with the Wilson derivative and the Stratonovitch prescription for this discretization leads to far better results at finite lattice spacing than other models with Wilson fermions considered in the literature. In particular, we check that fermionic and bosonic masses coincide and the unbroken Ward identities are fulfilled to high accuracy. Equally good results for the effective masses can be obtained in a model with the SLAC derivative (even without improvement terms). In two dimensions we introduce a non-standard Wilson term in such a way that the discretization errors of the kinetic terms are only of order O(a^2). Masses extracted from the corresponding manifestly supersymmetric model prove to approach their continuum values much quicker than those from a model containing the standard Wilson term. Again, a comparable enhancement can be achieved in a theory using the SLAC derivative.

hep-lat↗