Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice

Abstract

We continue to construct lattice super Yang-Mills theories along the line discussed in the previous papers \cite{sugino, sugino2}. In our construction of $\mathcal{N}=2,4$ theories in four dimensions, the problem of degenerate vacua seen in \cite{sugino} is resolved by extending some fields and soaking up would-be zero-modes in the continuum limit, while in the weak coupling expansion some surplus modes appear both in bosonic and fermionic sectors reflecting the exact supersymmetry. A slight modification to the models is made such that all the surplus modes are eliminated in two- and three-dimensional models obtained by dimensional reduction thereof. $\mathcal{N}=4,8$ models in three dimensions need fine-tuning of three and one parameters respectively to obtain the desired continuum theories, while two-dimensional models with $\mathcal{N}=4,8$ do not require any fine-tuning.

Comments: 28 pages, no figure, LaTeX, JHEP style; (v2) published version to JHEP; (v3) argument on the vacuum degeneracy revised, 34 pages