https://doi.org/10.1140/epjc/s10052-014-2976-2
Regular Article - Theoretical Physics
Generalized 
-deformed correlation functions as spectral functions of hyperbolic geometry
1
International School for Advanced Studies (SISSA/ISAS), Via Bonomea 265, 34136 , Trieste, Italy
2
INFN, Sezione di Trieste, Trieste, Italy
3
Departamento de Física, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina, Paraná, Brazil
4
Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza, s/n, Niterói-RJ CEP , 24210-346, Brazil
* e-mail: emilia@if.uff.br
Received:
20
May
2014
Accepted:
10
July
2014
Published online:
9
August
2014
We analyze 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. By definition p-dimensional MacMahon function, with 
, is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to 
. With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized 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.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
