### Abstract

We construct a lattice formulation of a mass-deformed two-dimensional N = (8, 8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)_{R} rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S^{2}. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N = 4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N = 4 super Yang-Mills on R^{4} without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

Original language | English |
---|---|

Pages (from-to) | 597-611 |

Number of pages | 15 |

Journal | Progress of Theoretical Physics |

Volume | 126 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 Oct |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*,

*126*(4), 597-611. https://doi.org/10.1143/PTP.126.597

**Two-dimensional lattice for four-dimensional N = 4 supersymmetric yang-mills.** / Hanada, Masanori; Matsuura, So; Sugino, Fumihiko.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 126, no. 4, pp. 597-611. https://doi.org/10.1143/PTP.126.597

}

TY - JOUR

T1 - Two-dimensional lattice for four-dimensional N = 4 supersymmetric yang-mills

AU - Hanada, Masanori

AU - Matsuura, So

AU - Sugino, Fumihiko

PY - 2011/10

Y1 - 2011/10

N2 - We construct a lattice formulation of a mass-deformed two-dimensional N = (8, 8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N = 4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N = 4 super Yang-Mills on R4 without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

AB - We construct a lattice formulation of a mass-deformed two-dimensional N = (8, 8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N = 4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N = 4 super Yang-Mills on R4 without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

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UR - http://www.scopus.com/inward/citedby.url?scp=80755126224&partnerID=8YFLogxK

U2 - 10.1143/PTP.126.597

DO - 10.1143/PTP.126.597

M3 - Article

AN - SCOPUS:80755126224

VL - 126

SP - 597

EP - 611

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 4

ER -