Speaker
Joel Giedt
(Rensselaer Polytechnic Institute)
Description
Formulations of lattice supersymmetry over the last decade
have been able to
significantly reduce the amount of fine-tuning necessary in
order to obtain the
correct continuum limit. In the case of N=4 super-Yang-Mills,
the approach that
has emerged as the best path forward is based on a
topological twisting of the theory.
We describe this lattice theory and the various studies we
have performed in order
to understand its renormalization. A discrete subgroup of the
R-symmetry has been
used to identify the supersymmetric continuum limit, and we
have performed nonpertubative
numerical tests of it. In terms of applications, Montonen and
Olive found evidence that
a duality could exist in Yang-Mills with adjoint
scalars. In this scheme, the 't Hooft-Polyakov monopole is
dual to the W boson,
leading to a theory equivalent to the Georgi-Glashow model
but with magnetic charge replacing
electric charge. The duality is believed to be realized in N=4
super-Yang-Mills. We are pursuing
numerical, nonperturbative evidence for this S-duality using
our lattice formulation.
The various tricks that are necessary for doing this will be
described.
