Correlators of Matrix Models on Homogeneous Spaces

Abstract

We investigate the correlators of TrA_{mu}A_{nu} in matrix models on homogeneous spaces: S^2 and S^2 x S^2. 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 S^2 x S^2 acquires a 4 dimensional fractal structure in contrast to fuzzy S^2. We also find that the two point functions exhibit logarithmic scaling violations.

26 pages, 2 figures, latex file, published version in Nucl. Phys. B

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Cited by in corpus (12)

• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• Perturbative dynamics of fuzzy spheres at large N
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Fuzzy Torus in Matrix Model
• Graviton Propagators on Fuzzy G/H
• Graviton Propagators in Supergravity and Noncommutative Gauge Theory
• Wilson Line Correlators in N=4 Non-commutative Gauge Theory on S^2 x S^2
• Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory
• Superstring vertex operators in type IIB matrix model
• D-dependence of gap between critical temperatures in one-dimensional gauge theories