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Correlators of matrix models on homogeneous spaces |
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| Authors: | Yoshihisa Kitazawa Yastoshi Takayama Dan Tomino |
| Affiliation: | aHigh Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan bDepartment of Particle and Nuclear Physics, Graduate University for Advanced Studies, Tsukuba, Ibaraki 305-0801, Japan cYukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan |
| Abstract: | We investigate the correlators of TrAμAν in matrix models on homogeneous spaces: S2 and S2×S2. Their expectation value is a good order parameter to measure the geometry of the space on which non-commutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum momentum. We develop an efficient procedure to calculate them through 1PI diagrams. We determine the large N scaling behavior of the correlators. The order parameter shows that fuzzy S2×S2 acquires a 4-dimensional fractal structure in contrast to fuzzy S2. We also find that the two point functions exhibit logarithmic scaling violations. |
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