Kontsevich-Witten Model From 2+1 Gravity: New Exact Combinatorial Solution

TL;DR

This paper derives a new exact combinatorial solution connecting 2+1 gravity partition functions with the Kontsevich-Witten model, revealing insights into the transition regimes of Riemann surfaces and applications beyond physics.

Contribution

It introduces a novel combinatorial approach to relate 2+1 gravity partition functions to the Kontsevich-Witten model, expanding understanding of geometric regimes.

Findings

Exact combinatorial solution for 2+1 gravity partition function

Recovery of Kontsevich's results using combinatorics

Potential applications to non-traditional fields

Abstract

In previous publications (J.Geom.Phys.38 (2001) 81-139 and references therein) the partition function for 2+1 gravity was constructed for the fixed genus Riemann surface. With help of this function the dynamical transition from pseudo-Anosov to periodic (Seifert-fibered) regime was studied.In this paper the periodic regime is studied in some detail in order to recover major results of Kontsevich (Comm.Math.Phys. 147 (1992) 1-23) ispired by earlier work by Witten on topological two dimensional quantum gravity.To achieve this goal some results from enumerative combinatorics have been used. The logical developments are extensively illustrated using geometrically convincing figures. This feature is helpful for development of some non traditional applications (mentioned through the entire text) of obtained results to fields other than theoretical particle physics