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Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

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arxiv 1109.6807 v2 pith:RXG65MD2 submitted 2011-09-30 hep-lat hep-th

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

classification hep-lat hep-th
keywords theorylatticesuperchargesfuzzymasstwo-dimensionalaroundminimum
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N = 2 U(k) SYM on R^2 x (Fuzzy R^2) around the minimum of k-coincident fuzzy spheres.

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