Exact lattice supersymmetry☆

Abstract

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.

Spin Chains with Dynamical Lattice Supersymmetry

“…In this case, we have γ j mn = (−1) j β j mn . Grouping together the terms containing on the one hand β j m+1,n , β j mn and β j+1 m,n+1 , β j+1 mn on the other, the identity is readily verified by using the explicit expressions (19) as well as the identity (25). As before, the work for j < −1 can be reduced to this case by using the symmetry of the coefficients under j → −j.…”

Baryonic states in supersymmetric Yang-Mills theory

“…Models that preserve part of an extended superalgebra are discussed in Ref. [10]. In our simulations, we use the "Curci-Veneziano" lattice action [11] where the gauge part (S g ) of the full action is given by the standard Wilson action…”

Introduction

“…On a different note, we conclude by mentioning -albeit not as much as it would deservethat recent years have also witnessed rapid progress in constructing lattice discretizations of supersymmetric gauge theories [246,249,250], in particular of the N = 4 SYM theory [251][252][253][254][255]. Large-scale calculations [256] have studied the static "interquark" potential [257,258] and the anomalous scaling dimension of the Konishi operator [259] (see also [246]).…”