On the connection between 2d topological gravity and the reduced Hermitian matrix model

Abstract

We discuss how concepts such as geodesic length and the volume of space-time can appear in 2d topological gravity. We then construct a detailed mapping between the reduced Hermitian matrix model and 2d topological gravity at genus zero. This leads to a complete solution of the counting problem for planar graphs with vertices of even coordination number. The connection between multi-critical matrix models and multi-critical topological gravity at genus zero is studied in some detail.

Correlators in the simplest gauge-string duality

“…Here d = i k i . This agrees with the enumeration of graphs in [28] (see also [29]). The nontrivial d dependence shows that the answers are not, in general, factorised.…”

“…It is a combinatorial challenge to work out the form of the polynomial. Surprisingly the answer is simple and given in [28] (see also [29])…”

Wilson loops in supersymmetric Yang–Mills theory from random matrix theory

“…Consider as an example the sixth-order (symmetric) potential from eq. (14). To leading order in 1/N 2 we get…”

“…There, a closed expression has been derived for all planar k-point correlators with k ≥ 2 [9,14]. All higher genus corrections in 1/N 2 are also available for both the complex [15] and reduced hermitian models [16].…”

“…(38) for m = 1, 2 by tuning the potential accordingly in eq. (14). For this special choice of coupling constants the Bessel functions in eq.…”