Formal multidimensional integrals, stuffed maps, and topological recursion

被引:22
|
作者
Borot, Gaetan [1 ]
机构
[1] MPI Math, Vivatsgasse 7, D-53111 Bonn, Germany
来源
关键词
Map enumeration; matrix models; 2D quantum gravity; loop equations; Tutte equation; topological recursion;
D O I
10.4171/AIHPD/7
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We show that the large N expansion in the multi-trace 1 formal hermitian matrix model is governed by the topological recursion of [24] with extra initial conditions. In terms of a 1d gas of eigenvalues, this model includes - on top of the squared Vandermonde - multilinear interactions of any order between the eigenvalues. In this problem, the initial data (omega(0)(1), omega(0)(2)) of the topological recursion is characterized: for omega(0)(1), by a non-linear, non-local Riemann-Hilbert problem on the discontinuity locus Gamma to determine; for omega(0)(2), by a related but linear, nonlocal Riemann-Hilbert problem on the discontinuity locus Gamma. In combinatorics, this model enumerates discrete surfaces (maps) whose elementary 2-cells can have any topology - omega(0)(1) being the generating series of disks and omega(0)(2) that of cylinders. In particular, by substitution one may consider maps whose elementary 2-cells are themselves maps, for which we propose the name "stuffed maps." In a sense, our results complete the program of the "moment method" initiated in the 90s to compute the formal 1/N expansion in the 1 hermitian matrix model.
引用
收藏
页码:225 / 264
页数:40
相关论文
共 50 条
  • [1] Simple Maps, Hurwitz Numbers, and Topological Recursion
    Borot, Gaetan
    Garcia-Failde, Elba
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, 380 (02) : 581 - 654
  • [2] Simple Maps, Hurwitz Numbers, and Topological Recursion
    Gaëtan Borot
    Elba Garcia-Failde
    Communications in Mathematical Physics, 2020, 380 : 581 - 654
  • [3] RECURSION-RELATIONS FOR MULTIDIMENSIONAL FRANCK-CONDON OVERLAP INTEGRALS
    RUHOFF, PT
    CHEMICAL PHYSICS, 1994, 186 (2-3) : 355 - 374
  • [4] Topological recursion, symplectic duality, and generalized fully simple maps
    Alexandrov, A.
    Bychkov, B.
    Dunin-Barkowski, P.
    Kazarian, M.
    Shadrin, S.
    JOURNAL OF GEOMETRY AND PHYSICS, 2024, 206
  • [5] THE FORMAL LANGUAGE OF RECURSION
    MOSCHOVAKIS, YN
    JOURNAL OF SYMBOLIC LOGIC, 1989, 54 (04) : 1216 - 1252
  • [6] Topological entropy for multidimensional perturbations of one-dimensional maps
    Misiurewicz, M
    Zgliczynski, P
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2001, 11 (05): : 1443 - 1446
  • [7] Topological recursion and geometry
    Borot, Gaeetan
    REVIEWS IN MATHEMATICAL PHYSICS, 2020, 32 (10)
  • [8] An overview of the topological recursion
    Eynard, Bertrand
    PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL III, 2014, : 1063 - 1085
  • [9] CFT and topological recursion
    Ivan Kostov
    Nicolas Orantin
    Journal of High Energy Physics, 2010
  • [10] Blobbed topological recursion
    G. Borot
    Theoretical and Mathematical Physics, 2015, 185 : 1729 - 1740