Simon Catterall (Syracuse University)

Supersymmetry on a lattice

Attempts to formulate supersymmetric field theories on discrete spacetime lattices have a long history. However, until recently most of these efforts have failed. In this talk I will review some of the new ideas that have finally allowed a solution to this problem for
certain supersymmetric theories. I will focus my attention, in particular, on N=4 super Yang-Mills which forms one of the pillars of the AdSCFT correspondence connecting gravitational theories in anti-deSitter space to gauge theories living on the boundary of that space.

I will present results on the first large scale lattice study of N=4 Yang-Mills using this new approach. Our results are consistent with the existence of a single deconfined phase for the theory in which the static potential shows only a Coulomb behavior. Unlike QCD there is no confining, chirally broken phase even at strong coupling. This is consistent with one loop calculations which show that the beta function of the lattice theory vanishes just as expected in the continuum.