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

Masanori Hanada, So Matsuura, Fumihiko Sugino

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)597-611
Number of pages15
JournalProgress of Theoretical Physics
Issue number4
Publication statusPublished - 2011 Oct

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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