Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry

TL;DR

This paper explores the connection between p-dimensional MacMahon functions, vertex operator algebras, and spectral functions of hyperbolic geometry, revealing new links between combinatorics, conformal field theory, and geometric spectral theory.

Contribution

It demonstrates that p-dimensional MacMahon functions can be expressed using Ruelle spectral functions related to hyperbolic geometry, bridging combinatorics and spectral geometry.

Findings

MacMahon functions are representable as 2D CFT amplitudes.

p-dimensional MacMahon functions relate to Ruelle spectral functions.

Spectrum encoded in Patterson-Selberg functions of hyperbolic 3-manifolds.

Abstract

We analyse the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite dimensional Lie algebras, MacMahon and Ruelle functions. A p-dimensional MacMahon function is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c=1 CFT. In this paper we show that p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three dimensional hyperbolic geometry.