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Prog. Theor. Phys. Vol. 126 No. 4 (2011) pp. 597-611

[ Full Text PDF : FREE ACCESS (181K) ]

Two-Dimensional Lattice for Four-Dimensional N = 4 Supersymmetric Yang-Mills

Masanori Hanada,1,2,* So Matsuura3,** and Fumihiko Sugino4,***

1Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel
2Department of Physics, University of Washington, Seattle, WA 98195-1560, USA
3Department of Physics, and Research and Education Center for Natural Science, Keio University, Yokohama 223-8521, Japan
4Okayama Institute for Quantum Physics, Okayama 700-0015, Japan

(Received August 5, 2011; Revised August 19, 2011)

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 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.

Subject Index : 100, 110, 125, 127, 138
URL : http://ptp.ipap.jp/link?PTP/126/597/
DOI : 10.1143/PTP.126.597


*E-mail: mhanada@u.washington.edu
**E-mail: s.matsu@phys-h.keio.ac.jp
***E-mail: fumihiko_sugino@pref.okayama.lg.jp

[ Full Text PDF : FREE ACCESS (181K) ] Citation:

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