Truncation of lattice N=4 super Yang-Mills
We describe our studies of truncation of the twisted formulation of four-dimensional lattice N=4 super Yang-Mills from U(N) gauge theory to SU(N) gauge theory. One approach involves imposing the constraint that the complexified bosonic link matrices are elements of the group SL(N,C). We describe how this is consistent with SU(N) lattice gauge invariance. The second approach achieves this objective dynamically by including a potential that drives the determinant of the link fields to unity. The latter formulation allows us to make the necessary arguments which show that the violation of the scalar supersymmetry in the lattice formulation due to this truncation is a 1/N^2 effect. We present numerical studies in four dimensions which provide concrete evidence for this conclusion, consisting of two supersymmetry Ward identities that are seen to be restored in the large N limit (up to 1% violations due to boundary conditions and a small soft mass term).
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