# zbMATH — the first resource for mathematics

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 $$S^2\times S^2$$.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T75 Noncommutative geometry methods in quantum field theory
BASES/SPRING
Full Text:
##### References:
 [1] Banks, T.; Fischler, W.; Shenker, S.H.; Susskind, L., M-theory as a matrix model: a conjecture, Phys. rev. D, 55, 5112, (1997) [2] Ishibashi, N.; Kawai, H.; Kitazawa, Y.; Tsuchiya, A., A large-N reduced model as superstring, Nucl. phys. B, 498, 467, (1997) · Zbl 0979.81567 [3] Connes, A.; Douglas, M.; Schwarz, A., Noncommutative geometry and matrix theory: compactification on tori, Jhep, 9802, 003, (1998) [4] Seiberg, N.; Witten, E., String theory and non-commutative geometry, Jhep, 9909, 032, (1999) [5] Myers, R.C., Dielectricbranes, Jhep, 9912, 022, (1999) [6] Alekseev, A.Y.; Recknagel, A.; Schomerus, V., Brane dynamics in background fluxes and noncommutative geometry, Jhep, 0005, 010, (2000) · Zbl 0992.81061 [7] Aoki, H.; Ishibashi, N.; Iso, S.; Kawai, H.; Kitazawa, Y.; Tada, T., Non-commutative yang – mills in IIB matrix model, Nucl. phys., 565, 176, (2000) · Zbl 0956.81089 [8] Li, M., Strings from IIB matrices, Nucl. phys. B, 499, 149, (1997) · Zbl 0934.81037 [9] Ishibashi, N.; Iso, S.; Kawai, H.; Kitazawa, Y., Wilson loops in non-commutative yang – mills, Nucl. phys. B, 573, 573, (2000) · Zbl 0947.81137 [10] Gross, D.J.; Hashimoto, A.; Itzhaki, N., Observables of non-commutative gauge theories, Adv. theor. math. phys., 4, 893, (2000) · Zbl 1011.81075 [11] Minwalla, S.; Raamsdonk, M.V.; Seiberg, N., Non-commutative perturbative dynamics, Jhep, 0002, 020, (2000) · Zbl 0959.81108 [12] Dhar, A.; Kitazawa, Y., Non-commutative gauge theory, open Wilson lines and closed strings, Jhep, 0108, 044, (2001) [13] Aoki, H.; Iso, S.; Kawai, H.; Kitazawa, Y.; Tada, T., Space – time structures from IIB matrix model, Prog. theor. phys., 99, 713, (1998) [14] Nishimura, J.; Vernizzi, G.; Anagnostopoulos, K.N.; Nishimura, J., New approach to the complex action problem and its application to a nonperturbative study of superstring theory, Jhep, Phys. rev. D, 66, 106008, (2002) [15] Nishimura, J.; Sugino, F., Dynamical generation of four-dimensional space – time in IIB matrix model, Jhep, 0205, 001, (2002) [16] Kawai, H.; Kawamoto, S.; Kuroki, T.; Matsuo, T.; Shinohara, S.; Kawai, H.; Kawamoto, S.; Kuroki, T.; Matsuo, T.; Shinohara, S., Improved perturbation theory and four-dimensional space – time in IIB matrix model, Nucl. phys. B, Prog. theor. phys., 109, 115-132, (2003) · Zbl 1031.81056 [17] Kitazawa, Y., Matrix models in homogeneous spaces, Nucl. phys. B, 642, 210, (2002) · Zbl 0998.81052 [18] Imai, T.A.; Kitazawa, Y.; Takayama, Y.; Tomino, D., Quantum corrections on fuzzy sphere, Nucl. phys. B, 665, 520, (2003) · Zbl 1059.81170 [19] Imai, T.; Kitazawa, Y.; Takayama, Y.; Tomino, D., Effective actions of matrix models on homogeneous spaces, Nucl. phys. B, 679, 143, (2004) · Zbl 1045.81530 [20] Kawabata, S., A new Monte Carlo event generator for high-energy physics, Comput. phys. commun., 41, 127, (1986), Also in Tsukuba Workshop: JLC 1990:239-0249 (QCD183:W82:1990) [21] Kawabata, S., A new version of the multidimensional integration and event generation package bases/spring, Comput. phys. commun., 88, 309-326, (1995), KEK-PREPRINT-94-197, KEK, Tsukuba, 1995 · Zbl 0888.65019 [22] Edmonds, A.R., Angular momentum in quantum mechanics, (1957), Princeton Univ. Press Princeton, NJ · Zbl 0079.42204 [23] Winger, E.P., Group theory, (1959), Academic Press New York [24] Ponzano, G.; Regge, T., Semiclassical limit of racah coefficients, Spectroscopic group theoretical methods in physics, (1968)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.