Strings in less than one dimension and the generalized KdV hierarchies. (English) Zbl 1332.81211
Summary: We find the differential equation satisfied by the exact specific heat for a series of models of matter coupled to 2D gravity, indexed by positive integers \(p\) and \(q\), and present evidence that they are the \(c<1\) minimal models with diagonal modular invariants.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 81T27 | Continuum limits in quantum field theory |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
References:
| [1] | Polyakov, A. M., Phys. lett. B, 103, 207 (1981) |
| [2] | Ambjørn, J.; Durhuus, B.; Fröhlich, J., Nucl. Phys. B, 257, 433 (1985), [FS14] |
| [3] | David, F., Nucl. Phys. B, 257, 45 (1985), [FS14] |
| [4] | Kazakov, V. A.; Kostov, I. K.; Migdal, A. A., Phys. Lett. B, 157, 295 (1985) |
| [5] | E. Brézin and V. Kazakov, ENS preprint (October 1989).; E. Brézin and V. Kazakov, ENS preprint (October 1989). |
| [6] | M. Douglas and S. Shenker, Rutgers preprint (October 1989).; M. Douglas and S. Shenker, Rutgers preprint (October 1989). |
| [7] | D. Gross and A. Migdal, Princeton preprint (October 1989).; D. Gross and A. Migdal, Princeton preprint (October 1989). |
| [8] | Kazakov, V. A., NBI-HE-89-25 (1989), Niels Bohr Institute, preprint |
| [9] | M. Staudacher, University of Illinois preprint (November 1989).; M. Staudacher, University of Illinois preprint (November 1989). |
| [10] | Kazakov, V. A., Phys. Lett. A, 119, 140 (1986) |
| [11] | E. Brézin, M. Douglas, V. Kazakov and S. Shenker, Rutgers preprint (December 1989).; E. Brézin, M. Douglas, V. Kazakov and S. Shenker, Rutgers preprint (December 1989). |
| [12] | D. Gross and A. Migdal, Princeton preprint (December 1989).; D. Gross and A. Migdal, Princeton preprint (December 1989). |
| [13] | Crnković, C.; Ginsparg, P.; Moore, G., YCTP-P20-89 (December 1989), Yale preprint |
| [14] | T. Banks, M. Douglas, N. Seiberg and S. Shenker, Rutgers preprint (december 1989).; T. Banks, M. Douglas, N. Seiberg and S. Shenker, Rutgers preprint (december 1989). |
| [15] | Mehta, M. L., Commun. Math. Phys., 79, 327 (1981) · Zbl 0471.28007 |
| [16] | Chadha, S.; Mahoux, G.; Mehta, M. L., J. Phys. A, 14, 579 (1981) |
| [17] | Douglas, M.; Shenker, S., (presentation at Soviet-American String Workshop (October 10-November 2, 1989), Princeton University: Princeton University Princeton, N.J) |
| [18] | Gel’fand, I. M.; Dikii, L. A., Russ. Math. Surv. 30, 5, 77 (1975) |
| [19] | Segal, G.; Wilson, G., Pub. Math IHES, 61, 5 (1985) · Zbl 0592.35112 |
| [20] | Boulatov, D. V.; Kazakov, V. A., Phys. Lett. B, 186, 379 (1987) |
| [21] | Drinfel’d, V. G.; Sokolov, V. V., J. Sov. Math., 1975 (1985) |
| [22] | Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B., Nucl. Phys. B, 241, 333 (1984) · Zbl 0661.17013 |
| [23] | I. Kostov, Saclay preprint SPhT 89-056.; I. Kostov, Saclay preprint SPhT 89-056. |
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