Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2004-10-23
JHEP0501:016,2005
Physics
High Energy Physics
High Energy Physics - Lattice
28 pages, no figure, LaTeX, JHEP style; (v2) published version to JHEP; (v3) argument on the vacuum degeneracy revised, 34 pag
Scientific paper
10.1088/1126-6708/2005/01/016
We continue to construct lattice super Yang-Mills theories along the line discussed in the previous papers \cite{sugino, sugino2}. In our construction of ${\cal N}=2, 4$ 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. ${\cal N}=4, 8$ models in three dimensions need fine-tuning of three and one parameters respectively to obtain the desired continuum theories, while two-dimensional models with ${\cal N}=4, 8$ do not require any fine-tuning.
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