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Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
Instanton partition functions N=2 SU(N) gauge theories general surface operator W-algebra duals
2011/3/2
We write down an explicit conjecture for the instanton partition functions in 4d N = 2 SU(N) gauge theories in the presence of a certain type of surface operator.
On the growth of restricted integer partition functions
integer partitions asymptotic growth
2010/12/10
We study the rate of growth of p(n, S,M), the number of partitions of n whose parts all belong to S and whose multiplicities all belong to M, where S (resp. M) are given infinite sets of positive (res...
Growth partition functions for cancellative infinite monoids
Growth partition functions cancellative infinite monoids
2010/12/15
We introduce the growth partition function Z,G(t)associated with any cancellative infinite monoid with a finite generator system G. It is a power series in t whose coefficients
l...
Benford's Law For Coefficients of Modular Forms and Partition Functions
Benford's Law Coefficients of Modular Forms Partition Functions
2010/11/30
Here we prove that Benford’s law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessa...
Canonical and grand canonical partition functions of Dyson gases as tau-functions of integrable hierarchies and their fermionic realization
partition functions integrable hierarchies Dyson gases
2010/4/2
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms o...
TOPOLOGICAL STRING PARTITION FUNCTIONS AS EQUIVARIANT INDICES
TOPOLOGICAL STRING PARTITION FUNCTIONS EQUIVARIANT INDICES
2018/4/20
We propose to use the identiˉcation of topological string partition functions as equivariant indices on framed moduli spaces of instantons to study the Gopakumar-Vafa conjecture for some local Calabi-...
T=0 Partition Functions for Potts Antiferromagnets on Square Lattice Strips with (Twisted) Periodic Boundary Conditions
Functions Potts Antiferromagnets Periodic Boundary Conditions
2010/11/2
We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graph...
Exact Potts Model Partition Functions on Ladder Graphs
Exact Potts Model Partition Functions Ladder Graphs
2010/11/2
We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder gr...