TY - JOUR

T1 - Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

AU - Hanada, Masanori

AU - Matsuura, So

AU - Sugino, Fumihiko

N1 - Funding Information:
The authors would like to thank Adi Armoni, Hikaru Kawai, Noboru Kawamoto, Jun Nishimura, Hidehiko Shimada, Hiroshi Suzuki, Asato Tsuchiya and Mithat Ünsal for discussions and enlightening comments. M.H. and F.S. would like to thank Weizmann Institute for Science where this work was initiated. The work of M.H. is supported from Postdoctoral Fellowship for Research Abroad by Japan Society for the Promotion of Science . The work of S.M. is supported in part by Grant-in-Aid for Young Scientists (B), 23740197 and Keio Gijuku Academic Development Funds . The work of F.S. is supported in part by Grant-in-Aid for Scientific Research (C), 21540290.

PY - 2012/4/21

Y1 - 2012/4/21

N2 - 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 R2×(Fuzzy R2) around the minimum of k-coincident fuzzy spheres.

AB - 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 R2×(Fuzzy R2) around the minimum of k-coincident fuzzy spheres.

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U2 - 10.1016/j.nuclphysb.2011.12.014

DO - 10.1016/j.nuclphysb.2011.12.014

M3 - Article

AN - SCOPUS:84855577835

SN - 0550-3213

VL - 857

SP - 335

EP - 361

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -