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

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.

arXiv comment12 pages, no figures

References in corpus (22)

• Quantum Gravity Partition Functions in Three Dimensions
• The Topological Vertex
• The Refined Topological Vertex
• Ground Ring Of Two Dimensional String Theory
• Quantum Foam and Topological Strings
• c=1 String as the Topological Theory of the Conifold
• W_{1+\infty} and W(gl_N) with central charge N
• Chern-Simons Theory and Topological Strings
• Lectures on Quantum Black Holes
• Quantum Calabi-Yau and Classical Crystals
• Boundary Partitions in Trees and Dimers
• Representation Theory of The $W_{1+\infty }$ Algebra
• Non-supersymmetric Black Holes and Topological Strings
• Partition Functions for Quantum Gravity, Black Holes, Elliptic Genera and Lie Algebra Homologies
• Crystal Melting and Black Holes
• Explicit Analysis of Kahler Deformations in 4D N=1 Supersymmetric Quiver Theories
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Topological string in harmonic space and correlation functions in $S^3$ stringy cosmology
• Refining the Shifted Topological Vertex
• String Partition Functions, Hilbert Schemes, and Affine Lie Algebra Representations on Homology Groups
• Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry
• Vertex Operators, ${\mathbb{C}}^3$ Curve and Topological Vertex

Cited by in corpus (1)

• Elliptic Genera and Characteristic $q$-Series of Superconformal Field Theory