Georg Bergner

Complete supersymmetry on the lattice and a No-Go theorem

In this work a lattice formulation of a supersymmetric theory is proposed and tested that preserves the complete supersymmetry on the lattice. The results of a onedimensional nonperturbative simulation show the realization of the full supersymmetry and the correct continuum limit of the theory. It is proven here that the violation of supersymmetry due to the absence of the Leibniz rule on the lattice can be amended only with a nonlocal derivative and nonlocal interaction term. The fermion doubling problem is also discussed, which leads to another important source of supersymmetry breaking on the lattice. This problem is also solved with a nonlocal realization.

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.

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 guarantees lattice supersymmetry, and compare the results for ordinary and nonstandard Wilson fermions with those for SLAC derivatives. It turns out that this improvement leads to better results for SLAC fermions but not for Wilson 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.

Infrared regime of SU(2) with one adjoint Dirac flavor

SU(2) gauge theory with one Dirac flavor in the adjoint representation is investigated on a lattice. Initial results for the gluonic and mesonic spectrum, static potential from Wilson and Polyakov loops, and the anomalous dimension of the fermionic condensate from the Dirac mode number are presented. The results found are not consistent with conventional confining behavior, pointing instead tentatively towards a theory lying within or very near the onset of the conformal window, with the anomalous dimension of the fermionic condensate in the range 0.9≲γ∗≲0.95. The implications of our work for building a viable theory of strongly interacting dynamics beyond the standard model are discussed.

The light bound states of supersymmetric SU(2) Yang-Mills theory

A bstractSupersymmetry provides a well-established theoretical framework for extensions of the standard model of particle physics and the general understanding of quantum field theories. We summarise here our investigations of N=1

Generalizing the Ginsparg-Wilson relation: Lattice supersymmetry from blocking transformations

\mathcal{N}=1

Compactified N = 1 supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition

supersymmetric Yang-Mills theory with SU(2) gauge symmetry using the non-perturbative first-principles method of numerical lattice simulations. The strong interactions of gluons and their superpartners, the gluinos, lead to confinement, and a spectrum of bound states including glueballs, mesons, and gluino-glueballs emerges at low energies. For unbroken supersymmetry these particles have to be arranged in supermultiplets of equal masses. In lattice simulations supersymmetry can only be recovered in the continuum limit since it is explicitly broken by the discretisation. We present the first continuum extrapolation of the mass spectrum of supersymmetric Yang-Mills theory. The results are consistent with the formation of super-multiplets and the absence of non-perturbative sources of supersymmetry breaking. Our investigations also indicate that numerical lattice simulations can be applied to non-trivial supersymmetric theories.

Phase structure of the \( \mathcal{N}=1 \) supersymmetric Yang-Mills theory at finite temperature

A bstractThe spectrum of particles in supersymmetric Yang-Mills theory is expected to contain a spin 1/2 bound state of gluons and gluinos, the gluino-glue particle. We study the mass of this particle in softly broken supersymmetric Yang-Mills theory on a lattice by means of numerical simulations. The main focus is the estimation of finite size effects. We extrapolate the mass first to the infinite volume and then to the limit of a vanishing gluino mass. The results indicate that finite size effects are tolerable on lattices of moderate size, and that remaining deviations from supersymmetry are probably due to finite lattice spacing effects.