Critical behavior of colored tensor models in the large N limit

被引:226
作者
Bonzom, Valentin [1 ]
Gurau, Razvan [1 ]
Riello, Aldo [2 ]
Rivasseau, Vincent [2 ]
机构
[1] Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada
[2] Univ Paris 11, CNRS UMR 8627, Phys Theor Lab, F-91405 Orsay, France
关键词
Random tensor models; 1/N expansion; FIELD-THEORY; GRAVITY;
D O I
10.1016/j.nuclphysb.2011.07.022
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
Colored tensor models have been recently shown to admit a large N expansion, whose leading order encodes a sum over a class of colored triangulations of the D-sphere. The present paper investigates in details this leading order. We show that the relevant triangulations proliferate like a species of colored trees. The leading order is therefore summable and exhibits a critical behavior, independent of the dimension. A continuum limit is reached by tuning the coupling constant to its critical value while inserting an infinite number of pairs of D-simplices glued together in a specific way. We argue that the dominant triangulations are branched polymers. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:174 / 195
页数:22
相关论文
共 55 条
[1]   The Jacobian conjecture as a problem of perturbative quantum field theory [J].
Abdesselam, A .
ANNALES HENRI POINCARE, 2003, 4 (02) :199-215
[2]   SUMMING OVER ALL GENERA FOR D-GREATER-THAN-1 - A TOY MODEL [J].
AMBJORN, J ;
DURHUUS, B ;
JONSSON, T .
PHYSICS LETTERS B, 1990, 244 (3-4) :403-412
[3]   THE APPEARANCE OF CRITICAL DIMENSIONS IN REGULATED STRING THEORIES [J].
AMBJORN, J ;
DURHUUS, B ;
FROHLICH, J ;
ORLAND, P .
NUCLEAR PHYSICS B, 1986, 270 (03) :457-482
[4]   Reconstructing the Universe [J].
Ambjorn, J ;
Jurkiewicz, J ;
Loll, R .
PHYSICAL REVIEW D, 2005, 72 (06)
[5]   3-DIMENSIONAL SIMPLICIAL QUANTUM-GRAVITY [J].
AMBJORN, J ;
VARSTED, S .
NUCLEAR PHYSICS B, 1992, 373 (02) :557-577
[6]   3-DIMENSIONAL SIMPLICIAL QUANTUM-GRAVITY AND GENERALIZED MATRIX MODELS [J].
AMBJORN, J ;
DURHUUS, B ;
JONSSON, T .
MODERN PHYSICS LETTERS A, 1991, 6 (12) :1133-1146
[7]  
Ambjorn J, 1996, FLUCTUATING GEOMETRIES IN STATISTICAL MECHANICS AND FIELD THEORY, P77
[8]   Nonperturbative 3D Lorentzian quantum gravity [J].
Ambjorn, J ;
Jurkiewicz, J ;
Loll, R .
PHYSICAL REVIEW D, 2001, 64 (04)
[9]   SCALING IN 4-DIMENSIONAL QUANTUM-GRAVITY [J].
AMBJORN, J ;
JURKIEWICZ, J .
NUCLEAR PHYSICS B, 1995, 451 (03) :643-676
[10]  
Ambjorn J, ARXIVGRQC0201028