N=1* Yang-Mills

KEKN=1*Yang-Mills()()()arXiv:0711.4235[hep-th]arXiv:08**.****[hep-th] in preparationIIB matrix model [Ishibashi-Kawai-Kitazawa-Tsuchiya]BFSS Matrix model [Banks-Fischler-Shenker-Susskind]Matrix string theory [Dijkgraaf-Verlinde-Verlinde]matrices

Nontrivial cyclesWilson loops

fields?[cf. Hanada-Kawai-Kimura][Kaneko-Kitazawa-Matsumoto][GI-Shimasaki-Takayama-Tsuchiya]S3N=4 SYM on RS3SYM on RS2Matrix T-duality/Large N reduction Plane wavematrix modelCommutative limit of fuzzy sphere1-loop [GI-Shimasaki-Takayama-Tsuchiya][Ishii-GI-Shimasaki-Tsuchiya] ()2-loop, 3-loop, , 2dYMN=1* BF theory on S2(2d YM on S2)N=1* Continuum limit of fuzzy sphereChern-Simons theory on S3Matrix T-duality/ Large N reductionExactN=1*BFCS [Ishii-GI-Ohta-Shimasaki-Tsuchiya]N=1* matrix modelBF+mass term (2 dim YM) on S2 N=1* fuzzy sphere Minahan-Polychronakos BF

(1) Fuzzy sphere (2) (3) (4) (1) : fuzzy sphere background

S2

S2BFbackgroundSU(2)(fuzzy sphere)

(2) : Background

fuzzy spherical harmonicsS2(monopole harmonics)

map[Wu-Yang][Grosse-Klimcik-Presnajder, Baez-Balachandran-Ydri-Vaidya, Dasgupta-SheikhJabbari-Raamsdonk,](3) : Fuzzy sphere

Blau-Tompson[][][]fuzzy spherical harmonics

(4) :

N=1* YM N=1* fuzzy sphere S2YMLocalization Matrix T-duality/Large N reduction S3(/Zk) Chern-Simons CS DYM N=1* Wilson loop [Ishii-GI-Ohta-Shimasaki-Tsuchiya]Wilson loop [Ishibashi-Iso-Kawai-Kitazawa]

commutative limit

[Ishii-GI-Shimasaki-Ohta-Tsuchiya] S3