PHASES OF THE LARGE-N MATRIX MODEL AND NONPERTURBATIVE EFFECTS IN 2D GRAVITY

被引:101
作者
DAVID, F
机构
[1] Service de Physique Théorique Laboratoire de la Direction des Sciences de la Matiére, Commissariat à l'Energie Atomique., CEN Saclay, Cedex
关键词
D O I
10.1016/0550-3213(91)90202-9
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
The large-N solution of the one-matrix model of E. Brezin, C. Itzykson, G. Parisi and J. B. Zuber is considered for generic complex potential. A regular large-N limit does not exist in some singular domain, which depends on the prescription chosen in order to make the matrix integral convergent at infinity. Near the m = 2 critical point the singular domain (in the scaling variable x complex plane) is a sector of angle 2-pi/5 coinciding with the sector of poles of the "triply truncated" Painleve I transcendent of Boutroux, which is therefore (although not real) the only solution of the string equation compatible with the matrix model and the loop equations for two-dimensional gravity. Our approach allows us to relate non-perturbative effects in the string equations to instantons in the matrix model and to discuss the flows between multicritical points.
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页码:507 / 524
页数:18
相关论文
共 30 条
[1]   DISEASES OF TRIANGULATED RANDOM SURFACE MODELS, AND POSSIBLE CURES [J].
AMBJORN, J ;
DURHUUS, B ;
FROHLICH, J .
NUCLEAR PHYSICS B, 1985, 257 (03) :433-449
[2]  
BACHAS C, 1990, CERNTH571490 PREPR
[3]  
BAHNOT G, 1990, IASSNSHEP9052 PREPR
[4]   A NONPERTURBATIVE AMBIGUITY FREE SOLUTION OF A STRING MODEL [J].
BREZIN, E ;
MARINARI, E ;
PARISI, G .
PHYSICS LETTERS B, 1990, 242 (01) :35-38
[5]   PLANAR DIAGRAMS [J].
BREZIN, E ;
ITZYKSON, C ;
PARISI, G ;
ZUBER, JB .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 59 (01) :35-51
[6]   EXACTLY SOLVABLE FIELD-THEORIES OF CLOSED STRINGS [J].
BREZIN, E ;
KAZAKOV, VA .
PHYSICS LETTERS B, 1990, 236 (02) :144-150
[7]  
Cicuta G. M., 1986, MOD PHYS LETT, V01, P125
[8]   ISING-MODELS ON FEYNMAN GRAPHS [J].
CICUTA, GM ;
MOLINARI, L ;
MONTALDI, E .
NUCLEAR PHYSICS B, 1988, 300 (02) :197-206
[9]   PLANAR DIAGRAMS, TWO-DIMENSIONAL LATTICE GRAVITY AND SURFACE MODELS [J].
DAVID, F .
NUCLEAR PHYSICS B, 1985, 257 (01) :45-58
[10]   LOOP EQUATIONS AND NONPERTURBATIVE EFFECTS IN 2-DIMENSIONAL QUANTUM-GRAVITY [J].
DAVID, F .
MODERN PHYSICS LETTERS A, 1990, 5 (13) :1019-1029