Nuclear Physics B319 (1989) 307-341
North-Holland, Amsterdam
A LOCAL INTERACTIVE LATHCE MODEL
WITH SUPERSYMMETRY
Maarten F.L. GOLTERMAN *t
Physics Department, University of California, Davis, CA 95616 USA
Donald N. PETCHER**
Supercomputer Computations Research Institute, Florida State University,
Tallahassee, FL 32306 USA
Received 28 March 1988
(Revised 10 October 1988)
A local euclidean lattice version of the two dimensional Wess-Zumino model is shown to be
supersymmetric in the quantum continuum limit to all orders in perturbation theory. Ward
identities resulting from a lattice generalization of the continuum supersymmetry are used as a
guide in the derivation.
1. Introduction
Supersymmetry has become very popular in recent years, not only as a beautiful
mathematical construct, but also as a candidate for providing the framework in
which to understand the unification of all forces of nature. As such, a non-perturba-
tive method for studying supersymmetric theories would be desirable for studying
such questions as spontaneous symmetry breaking which cannot be easily addressed
in perturbation theory.
Euclidean lattice theory has proved to be a fruitful ground for studying field
theory in a non-perturbative context ever since the introduction of the first lattice
gauge theory [1-3]. This step opened up the possibility of applying all the tools
which had already been developed for studying lattice systems in statistical mechan-
ics to the study of quantum gauge field theory. The great achievement in this work
was the accomplishment of a lattice regularization which respected the gauge
symmetry of the continuum theory so that the theory could be studied without fear
of introducing new problems resulting from an explicit gauge symmetry breaking.
The problem of putting a supersymmetric theory on a lattice is substantially
different from that of a gauge theory, because supersymmetry is not an internal
* Address: Department of Physics, U.C.L.A., Los Angeles, CA 90024-1547, USA.
t Supported by the Department of Energy.
** Supported by the Florida State University Supercomputer Computations Research Institute which is
partially funded by the Department of Energy through Contract No. DE-FC05-85ER250000.
0550-3213/89/$03.50©Elsevier Science Publishers B.V.
(North-Holland Phvsies Publi~hin~ Divi~inn~