### Abstract

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.

Original language | English |
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Pages (from-to) | 335-361 |

Number of pages | 27 |

Journal | Nuclear Physics B |

Volume | 857 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 Apr 21 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*857*(3), 335-361. https://doi.org/10.1016/j.nuclphysb.2011.12.014

**Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges.** / Hanada, Masanori; Matsuura, So; Sugino, Fumihiko.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 857, no. 3, pp. 335-361. https://doi.org/10.1016/j.nuclphysb.2011.12.014

}

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

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.

UR - http://www.scopus.com/inward/record.url?scp=84855577835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855577835&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2011.12.014

DO - 10.1016/j.nuclphysb.2011.12.014

M3 - Article

VL - 857

SP - 335

EP - 361

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -