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Some aspects of large- theories
Rev. Mod. Phys. 59, 235 – Published 1 January, 1987
DOI: https://doi.org/10.1103/RevModPhys.59.235
Abstract
This is a pedagogical review of some aspects of quantum field theories in the limit in which the number of internal degrees of freedom is large. The focus is on large- QCD. The authors briefly discuss several well-known approaches to a solution of the limit: loop equations, classical actions, and master fields. Eguchi-Kawai models are discussed in detail, and some recently obtained numerical results are reviewed.
References (127)
- Adkins, G., C. R. Nappi, and E. Witten, 1983, Nucl. Phys. B 228, 552
- Alfaro, J., and B. Sakita, 1982, Phys. Lett. B 116, 57
- Aneva, B., Y. Brihaye, and P. Rossi, 1984, Phys. Lett. B 134, 245
- Balachandran, A. P., V. P. Nair, S. G. Rajeev, and A. Stern, 1982, Phys. Rev. Lett. 49, 1124
- Bardakci, K., 1981a, Nucl. Phys. B 178, 263
- Bardakci, K., 1981b, Nucl. Phys. B 193, 245
- Bardakci, K., 1982, Nucl. Phys. B 194, 349
- Bars, I., M. Gunaydin, and S. Yankelowicz, 1983, Nucl. Phys. B 219, 81
- Batrouni, G., and B. Svetitsky, 1984, Phys. Rev. Lett. 52, 2205
- Belova, T. I., Yu. M. Makeenko, M. I. Polikarpov, and A. I. Veslov, 1984, Nucl. Phys. B 230, 473
- Bhanot, G., 1983, Phys. Lett. B 120, 371
- Bhanot, G., U. Heller, and H. Neuberger, 1982a, Phys. Lett. B 113, 47
- Bhanot, G., U. Heller, and H. Neuberger, 1982b, Phys. Lett. B 115, 237
- Bhanot, G., and K. J. M. Moriarty, 1983, Phys. Lett. B 122, 271
- Bhanot, G., and Rebbi, 1981, Phys. Rev. D 24, 3319
- Brihaye, Y., G. Maiella, and P. Rossi, 1983, Nucl. Phys. B 222, 309
- Brown, F., and L. Yaffe, 1986, Nucl. Phys. B 271, 267
- Carlson, J. W., 1983, Phys. Lett. B 127, 115
- Celik, T., J. Engels, and H. Satz, 1983, Phys. Lett. B 125, 411
- Chen, T. L., C. I. Tan, and X. T. Zheng, 1982, Phys. Lett. B 116, 419
- Coleman, S., 1982, in Pointlike Structures Inside and Outside Hadrons, Erice Lectures of 1979, edited by A. Zichichi (Plenum, New York), p. 11
- Creutz, M., 1980, Phys. Rev. Lett. 45, 313
- Das, S. R., 1983, Phys. Lett. B 132, 155
- Das, S. R., and J. B. Kogut, 1984a, Nucl. Phys. B 235 [FS11], 521
- Das, S. R., and J. B. Kogut, 1984b, Phys. Lett. B 141, 105
- Das, S. R., and J. B. Kogut, 1984c, Phys. Lett. B 145, 375
- Das, S. R., and J. B. Kogut, 1985a, Nucl. Phys. B 257, 141
- Das, S. R., and J. B. Kogut, 1985b, Phys. Rev. D 31, 2704
- Das, S. R., and S. R. Wadia, 1982, Phys. Lett. B 117, 228
- Dhar, A., and S. R. Wadia, 1984, Phys. Rev. Lett. 52, 959
- Eguchi, T., 1979, Phys. Lett. B 87, 91
- Eguchi, T., 1983, in Non-Perturbative Field Theory and QCD, Proceedings of the Trieste Workshop, edited by R. Iengo, A. Neveu, P. Olesen, and G. Parisi (World Scientific, Singapore), p. 128
- Eguchi, T., and H. Kawai, 1982, Phys. Rev. Lett. 48, 1063
- Eguchi, T., and R. Nakayama, 1983, Phys. Lett. B 122, 59
- Fabricius, K., and C. P. Korthals-Altes, 1984, Nucl. Phys. B 240, 237
- Fabricius, K., and C. P. Korthals-Altes, 1986, Nucl. Phys. B 269, 97
- Fabricius, K., and O. Haan, 1983, Phys. Lett. B 131, 399
- Fabricius, K., and O. Haan, 1984, Phys. Lett. B 139, 293
- Fabricius, K., and O. Haan, 1985, Nucl. Phys. B 260, 285
- Fabricius, K., O. Haan, and T. Filk, 1984, Phys. Lett. B 144, 240
- Fabricius, K., O. Haan, and F. Klinkhamer, 1984, Phys. Rev. D 30, 2227
- Foerster, D., 1979, Phys. Lett. B 87, 87
- Gervais, J. L., and A. Neveu, 1979, Nucl. Phys. B 153, 445
- Gocksch, A., 1985, Phys. Rev. Lett. 55, 1446
- Gocksch, A., and F. Neri, 1983, Phys. Rev. Lett. 50, 1099
- Gocksch, A., F. Neri, and P. Rossi, 1983, Phys. Lett. B 130, 407
- Gocksch, A., F. Neri, and P. Rossi, 1984, Nucl. Phys. B 238, 674
- Gocksch, A., and M. Okawa, 1984, Phys. Rev. Lett. 52, 1751
- Gonzales-Arroyo, A., and C. P. Korthals-Altes, 1983, Phys. Lett. 131B, 396
- Gonzales-Arroyo, A., and M. Okawa, 1983a, Phys. Rev. D 27, 2397
- Gonzales-Arroyo, A., and M. Okawa, 1983b, Phys. Lett. B 133, 415
- Gonzales-Arroyo, A., and M. Okawa, 1984, Nucl. Phys. B 247, 104
- Green, F., 1983, Phys. Lett. B 124, 501
- Green, F., and F. Karsch, 1984, Nucl. Phys. B 238, 297
- Green, F., and S. Samuel, 1981, Nucl. Phys. B 190 [FS3], 113
- Greensite, J., and M. B. Halpern, 1983, Nucl. Phys. B 211, 343
- Gross, D., and Y. Kitazawa, 1982, Nucl. Phys. B 206, 440
- Gross, D., and E. Witten, 1980, Phys. Rev. D 21, 446
- Gross, M., and J. Wheater, 1984, Nucl. Phys. B 240, 253
- Haan, O., 1981, Phys. Lett. B 106, 207
- Halpern, M. B., 1980, Nucl. Phys. B 173, 504
- Halpern, M. B., 1981, Nucl. Phys. B 188, 61
- Heller, U., and H. Neuberger, 1982a, Nucl. Phys. B 207, 399
- Heller, U., and H. Neuberger, 1982b, Phys. Rev. Lett. 49, 621
- Heller, U., and H. Neuberger, 1984, Phys. Rev. D 30, 498
- 't Hooft, G., 1974, Nucl. Phys. B 72, 461
- 't Hooft, G., 1981, Commun. Math. Phys. 81, 267
- Jevicki, A., and H. Levine, 1981, Ann. Phys. (N.Y.) 136, 113
- Jevicki, A., and N. Papanicolaou, 1980, Nucl. Phys. B 171, 362
- Jevicki, A., and J. P. Rodrigues, 1984, Nucl. Phys. B 230, [FS10], 317
- Jevicki, A., and B. Sakita, 1980, Nucl. Phys. B 165, 511
- Jevicki, A., and B. Sakita, 1981, Nucl. Phys. B 185, 89
- Karsch, F., 1982, Nucl. Phys. B 205 [FS5], 285
- Kennedy, A. D., J. Kuti, S. Meyer, and B. Pendleton, 1985, Phys. Rev. Lett. 54, 87
- Kitazawa, Y., and S. R. Wadia, 1983, Phys. Lett. B 120, 377
- Klinkhamer, F., 1983a, Nucl. Phys. B 218, 32
- Klinkhamer, F., 1983b, Nucl. Phys. B 228, 65
- Klinkhamer, F., 1984a, Z. Phys. C 21, 365
- Klinkhamer, F., 1984b, Z. Phys. C 21, 391
- Klinkhamer, F., 1984c, Nucl. Phys. B 240 [FS12], 270
- Klinkhamer, F., and P. van Baal, 1984, Nucl. Phys. B 237, 274
- Kogut, J., H. Matsuoka, M. Stone, H. W. Wyld, S. Shenker, J. Shigemitsu, and D. Sinclair, 1983, Phys. Rev. Lett. 51, 869
- Kuti, J., J. Poloyni, and K. Szlachanyi, 1981, Phys. Lett. B 98, 199
- Levine, H., and H. Neuberger, 1982a, Phys. Lett. B 119, 183
- Levine, H., and H. Neuberger, 1982b, Phys. Rev. Lett. 49, 1603
- Makeenko, Yu. M., and A. A. Migdal, 1979, Phys. Lett. B 88, 135
- Makeenko, Yu. M., and Polikarpov, 1982, Nucl. Phys. B 205 [FS5], 386
- Makeenko, Yu. M., M. I. Polikarpov, and A. I. Veslov, 1982, Phys. Lett. B 118, 133
- Marchesini, G., 1984, in Gauge Theory on a Lattice: 1984, Proceedings of the Argonne National Laboratory Workshop, edited by C. Zachos, W. Celmaster, E. Kovacs, and D. Sivers (Argonne National Laboratory, Argonne, Illinois), p. 270
- McLerran, L., and B. Svetitsky, 1981, Phys. Lett. B 98, 15
- Migdal, A. A., 1982, Phys. Lett. B 116, 425
- Migdal, A. A., 1983, Phys. Rep. C 102, 200
- Migdal, A. A., M. I. Polikarpov, and A. I. Veselov, and V. P. Yurov, 1984, Phys. Lett. B 135, 145
- Nambu, Y., 1979, Phys. Lett. B 80, 372
- Neuberger, H., 1982, Phys. Lett. B 119, 179
- Neuberger, H., 1983, Nucl. Phys. B 220 [FS8], 237
- Okawa, M., 1982a, Phys. Rev. Lett. 49, 353
- Okawa, M., 1982b, Phys. Rev. Lett. 49, 705
- Ogilvie, M., 1984, Phys. Rev. Lett. 52, 1369
- Parisi, G., 1982, Phys. Lett. B 112, 228
- Parisi, G., and Y. S. Wu, 1981, Sci. Sin. 24, 483
- Parisi, G., and Y. Zhang, 1983, Nucl. Phys. B 216, 408
- Pietarinen, E., 1981, Nucl. Phys. B 190, 349
- Pisarski, R., 1984, Phys. Rev. D 29, 1222
- Polyakov, A. M., 1979, Phys. Lett. B 82, 247
- Polyakov, A. M., and P. B. Wiegmann, 1983, Phys. Lett. B 131, 121
- Rodrigues, J. P., 1985, Nucl. Phys. B 260, 350
- Sakita, B., 1980, Phys. Rev. D 21, 1067
- Samuel, S., 1982, Phys. Lett. B 112, 237
- Skyrme, T. H., 1961, Proc. R. Soc. London, Ser. A 260, 127
- Svetitsky, B., and F. Fucito, 1983, Phys. Lett. B 131, 165
- Svetitsky, B., and L. Yaffe, 1982, Nucl. Phys. B 210, [FS6], 423
- van Baal, P., 1983, Commun. Math. Phys. 81, 267
- Veneziano, G., 1976, Nucl. Phys. B 117, 519
- Wadia, S. R., 1979, A Study of U (N) Lattice Gauge Theory in Two Dimensions, EFI Report No. 79-44
- Wadia, S. R., 1981a, Phys. Lett. B 93, 403
- Wadia, S. R., 1981b, Phys. Rev. D 24, 970
- Weingarten, D., 1979, Phys. Lett. B 87, 95
- Wess, J., and B. Zumino, 1971, Phys. Lett. B 37, 95
- Wheater, J., and M. Gross, 1984, Phys. Lett. 144B, 409
- Witten, E., 1979a, Nucl. Phys. B 160, 57
- Witten, E., 1979b, Nucl. Phys. B 156, 269
- Witten, E., 1980, Recent Developments in Gauge Theories, Proceedings of the Cargèse Summer Institute, 1979, edited by G. 't Hooft (NATO Advanced Study Institute Series—Series B: Physics, Vol. 59) (Plenum, New York)
- Witten, E., 1983a, Nucl. Phys. B 223, 422
- Witten, E., 1983b, Nucl. Phys. B 223, 433
- Yaffe, L., 1982, Rev. Mod. Phys. 54, 407
- Yaffe, L., 1984, private communication