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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.
We construct the wave functions in the q-deformed 2d Yang-Mills theory that compute torus correlation functions of affine currents in the VOA associated to a class of 4d $N = 2$ SCFTs. These wave functions are then shown to reduce to the topological
We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straig
Gauged N=8 supergravity in four dimensions is now known to admit a deformation characterized by a real parameter $omega$ lying in the interval $0leomegale pi/8$. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full N=8
In this article we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson-fermion correspondence, the analytic torsion, the Chern-Simons and $eta$ invariants, as well as the generation function associated to
We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the $lambda Tbar T$ deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each field, with a Dir