Lattice study of the two-dimensional Wess-Zumino model (original) (raw)

Supersymmetry breaking in two dimensions: The lattice N=1 Wess-Zumino model

Physical Review D, 2004

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.

Exact lattice supersymmetry: The two-dimensional N=2 Wess-Zumino model

Physical Review D, 2002

We study the two-dimensional Wess-Zumino model with extended N = 2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving exactly a single supersymmetric invariance at finite lattice spacing a. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to O(ga 2 ) where g is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the massgaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing. 0 Corresponding author: Simon Catterall,

Exact lattice supersymmetry at the quantum level for N = 2 Wess–Zumino models in 1- and 2-dimensions

International Journal of Modern Physics A, 2016

Supersymmetric lattice Ward–Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of [Formula: see text] 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.

Two-dimensional Wess-Zumino models at intermediate couplings

Physical Review D, 2008

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.

Supersymmetric lattice models in one and two dimensions

2007

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

Lattice Wess-Zumino model with Ginsparg-Wilson fermions: One-loop results and GPU benchmarks

Physical Review D, 2010

We numerically evaluate the one-loop counterterms for the four-dimensional Wess-Zumino model formulated on the lattice using Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U (1) R symmetry is exactly preserved in the limit of vanishing bare mass. We confirm previous findings by other authors that at one loop there is no renormalization of the superpotential in the lattice theory, but that there is a mismatch in the wavefunction renormalization of the auxiliary field. We study the range of the Dirac operator that results when the auxiliary fermion is integrated out, and show that localization does occur, but that it is less pronounced than the exponential localization of the overlap operator. We also present preliminary simulation results for this model, and outline a strategy for nonperturbative improvement of the lattice supercurrent through measurements of supersymmetry Ward identities. Related to this, some benchmarks for our graphics processing unit code are provided. Our simulation results find a nearly vanishing vacuum expectation value for the auxiliary field, consistent with approximate supersymmetry at weak coupling.

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

2008

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

A two-dimensional lattice model with exact supersymmetry

Nuclear Physics B - Proceedings Supplements, 2002

Starting from a simple discrete model which exhibits a supersymmetric invariance we construct a local, interacting, two-dimensional Euclidean lattice theory which also admits an exact supersymmetry. This model is shown to correspond to the Wess-Zumino model with extended N = 2 supersymmetry in the continuum. We have performed dynamical fermion simulations to check the spectrum and supersymmetric Ward identities and find good agreement with theory.

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

Physical Review D, 2011

We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U (1) R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.