4,155 research outputs found
Generalized Penner model and the Gaussian beta ensemble
In this paper, a new expression for the partition function of the generalized
Penner model given by Goulden, Harer and Jackson is derived. The Penner and the
orthogonal Penner partition functions are special cases of this formula. The
parametrized Euler characteristic deduced from our expression
of the partition function is shown to exhibit a contribution from the orbifold
Euler characteristic of the moduli space of Riemann surfaces of genus , with
punctures, for all parameters and odd. The other contributions
for even are linear combinations of the Bernoulli polynomials at rational
arguments. It turns out that the free energy coefficients of the generalized
Penner model in the continuum limit, are identical to those coefficients in the
large expansion of the Gaussian -ensemble. Moreover, the duality
enjoyed by the generalized Penner model, is also the duality symmetry of the
Gaussian -ensemble. Finally, a shift in the 't Hooft coupling constant
required by the refined topological string, would leave the Gaussian
-ensemble duality intact. This duality is identified with the remarkable
duality of the string at radius .Comment: 17 pages. arXiv admin note: text overlap with arXiv:1209.081
Chern-Simons Gauge Theories At Large , Penner Models And The Gauge Group Volumes
We construct a deformed Penner generating function responsible for
the close connection between Chern-Simons gauge theories at large
and the Penner models. This construction is then shown to follow from a
sector of a Chern-Simons gauge theory with coupling constant . The
free energy and its continuum limit of the perturbative Chern-Simons gauge
theory are obtained from the Penner model. Finally, asymptotic expansions for
the logarithm of the gauge group volumes are given for every genus
and shown to be equivalent to the continuum limits of the Chern-Simons
gauge theories and the Penner modelsComment: 19 pages; Progress of Theoretical Physics, Vol. 127, No. 2, February
201
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