Universal correlators for multi-arc complex matrix models. (English) Zbl 0925.81270
Summary: The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the Hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and Hermitian model.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
Keywords:
correlation functions; universality classes; eigenvalue density; Hermitian model; iterative loop equation solutionReferences:
| [1] | Brézin, E.; Zee, A., Nucl. Phys. B, 402, 613 (1993) · Zbl 1043.82534 |
| [2] | Kanzieper, E.; Freilikher, V., Phys. Rev. Lett., 78, 3806 (1997) · Zbl 1042.82552 |
| [3] | Shuryak, E. V.; Verbaarschot, J. J.M., Nucl. Phys. A, 560, 306 (1993) |
| [4] | Ambjørn, J.; Jurkiewicz, J.; Makeenko, Yu., Phys. Lett. B, 251, 517 (1990) |
| [5] | Ambjørn, J.; Kristjansen, C. F.; Makeenko, Yu., Mod. Phys. Lett. A, 7, 3187 (1992) · Zbl 1021.81779 |
| [6] | Ambjørn, J.; Chekhov, L.; Kristjansen, C. F.; Makeenko, Yu., Nucl. Phys. B, 404, 127 (1993) · Zbl 1043.81636 |
| [7] | Akemann, G.; Ambjørn, J., J. Phys. A, 29, L555 (1996) · Zbl 0902.15015 |
| [8] | Akemann, G., Nucl. Phys. B, 482, 403 (1996) · Zbl 0925.81311 |
| [9] | Dijkgraaf, R.; Verlinde, H.; Verlinde, E., Nucl. Phys. B, 348, 435 (1991) |
| [10] | Makeenko, Yu., An explicit solution of 2d topological gravity (August 1991), unpublished |
| [11] | Hollowood, I.; Miramontes, L.; Nappi, C.; Pasquinucci, A., Nucl. Phys. B, 373, 247 (1992) |
| [12] | Brower, R. C.; Deo, N.; Jain, S.; Tan, C., Nucl. Phys. B, 405, 166 (1993) · Zbl 0990.81634 |
| [13] | Morita, Y.; Hatsugai, Y.; Kohmoto, M., Phys. Rev. B, 52, 4716 (1995) |
| [14] | Beenakker, C. W.T, Nucl. Phys. B, 422, 515 (1994) |
| [15] | Itoi, C., Nucl. Phys. B, 493, 651 (1997) · Zbl 0933.82002 |
| [16] | Higuchi, S.; Itoi, C.; Nishigaki, S.; Sakai, N., Phys. Lett. B, 398, 123 (1997) |
| [17] | Akemann, G., Loop equations for multi-cut matrix models (March 1995), ITP-UH-11-95, DESY 95-066, hep-th/9503185 |
| [18] | Dalley, S.; Johnson, C.; Morris, T., Nucl. Phys. B, 368, 625 (1992) |
| [19] | David, F., Nucl. Phys. B, 348, 507 (1991) |
| [20] | Byrd, P. E.; Friedman, M. D., (Handbook of Elliptic Integrals for Engineers and scientists (1971), Springer: Springer New York) · Zbl 0213.16602 |
| [21] | Eynard, B.; Kristjansen, C. F., Nucl. Phys. B, 466, 463 (1996) · Zbl 1002.81521 |
| [22] | Ambjørn, J.; Kristjansen, C. F.; Makeenko, Yu., Phys. Rev. D, 50, 5193 (1994) |
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