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Stability of fuzzy \(S^2\times S^2\) geometry in IIB matrix model. (English) Zbl 1107.81322
Summary: We continue our study of the IIB matrix model on fuzzy \(S^2\times S^2\) [T. Imai et al., Nucl. Phys. B 665, No. 1-3, 520–544 (2003; Zbl 1059.81170 ); ibid. 679, No. 1-2, 143–167 (2004; Zbl 1045.81530)]. Especially in this paper we focus on the case where the size of one of \(S^2\times S^2\) is different from the other. By the power counting and SUSY cancellation arguments, we can identify the ’t Hooft coupling and large \(N\) scaling behavior of the effective action to all orders. We conclude that the most symmetric \(S^2\times S^2\) configuration where the both \(S^2\)s are of the same size is favored at the two-loop level. In addition, we develop a new approach to evaluate the amplitudes on fuzzy \(S^2\times S^2\).

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T75 Noncommutative geometry methods in quantum field theory
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