Removal of the trace mode in lattice N=4 super Yang-Mills theory

Twisted and orbifold formulations of lattice N=4 super Yang-Mills theory which possess an exact supersymmetry require a U(N)=SU(N)- U(1) gauge group. In the naive continuum limit, the U(1) modes trivially decouple and play no role in the theory. However, at nonzero lattice spacing they couple to the SU(N) modes and can drive instabilities in the lattice theory. For example, it is well known that the lattice U(1) theory undergoes a phase transition at strong coupling to a chirally broken phase. An improved action that suppresses the fluctuations in the U(1) sector was proposed in Catterall and Schaich [J. High Energy Phys. 07 (2015) 057JHEPFG1029-847910.1007/JHEP07(2015)057]. Here, we explore a more aggressive approach to the problem by adding a term to the action which can entirely suppress the U(1) mode. The penalty is that the new term breaks the Q-exact lattice supersymmetry. However, we argue that the term is 1/N2 suppressed and the existence of a supersymmetric fixed point in the planar limit ensures that any supersymmetry-violating terms induced in the action possess couplings that also vanish in this limit. We present numerical results on supersymmetric Ward identities consistent with this conclusion.