相关论文: BPS state counting on singular varieties

The purpose of this paper is to present a collection of interesting generating functions for partitions which have connections to positive definite binary quadratic forms. In establishing our results we obtain some new Bailey pairs.

We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…

We study rank $r$ cohomological Donaldson-Thomas theory on a toric Calabi-Yau orbifold of $\mathbb{C}^4$ by a finite abelian subgroup $\mathsf\Gamma$ of $\mathsf{SU}(4)$, from the perspective of instanton counting in cohomological gauge…

Hadronic decays of $B$ mesons are reviewed. First, masses of $B$ mesons and observed patterns together with physics behind them are discussed. Then the effective Hamiltonian responsible for major decays is presented and its practical…

We use the method of spectral networks to compute BPS state degeneracies in the Minahan-Nemeschansky $E_6$ theory, on its Coulomb branch, without turning on a mass deformation. The BPS multiplicities come out in representations of the $E_6$…

In this paper, we investigate decompositions of the partition function $p(n)$ from the additive theory of partitions considering the famous M\"{o}bius function $\mu(n)$ from multiplicative number theory. Some combinatorial interpretations…

We offer new Tauberian theorems for a generalized partition function as our main result. Our analysis provides insight into asymptotic behavior of power series with arithmetic functions as coefficients.

A functional theory based on single-particle occupation numbers is developed for pairing. This functional, that generalizes the BCS approach, directly incorporates corrections due to particle number conservation. The functional is…

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…

We introduce a new type of partitions that consists of partitions whose different parts alternate in parity (e.g., $3+2+2+1+1$). Various properties of this partition function are studied. In particular, we obtain its asymptotic behavior by…

We study the fusion of conformal interfaces in the c=1 conformal field theory. We uncover an elegant structure reminiscent of that of black holes in supersymmetric theories. The role of the BPS black holes is played by topological…

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…

Topologically ordered states are characterized by topological quantities like the Hall conductance, topological entanglement entropy, and chiral central charge. Techniques based on the modular Hamiltonian have recently been developed to…

Stanley generalized MacMahon's classical theorem by proving a product formula for the norm-trace generating function for plane partition with unbounded parts. In his recent work on biothorgonal polynomials, Kamioka proved a finite analogue…

Every partition of [[omega_1]^{< omega}]^2 into finitely many pieces has a cofinal homogeneous set. Furthermore, it is consistent that every directed partially ordered set satisfies the partition property if and only if it has finite…

We use sums over integer compositions analogous to generating functions in partition theory, to express certain partition enumeration functions as sums over compositions into parts that are $k$-gonal numbers; our proofs employ Ramanujan's…

We investigate the connections between flavored quivers, dimer models, and BPS pyramids for generic toric Calabi-Yau threefolds from various perspectives. We introduce a purely field theoretic definition of both finite and infinite pyramids…

A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The…

We study BPS bound states of little strings in a limit where they realise monopole strings in five dimensional gauge theories. The latter have gauge group $U(M)^N$ and arise from compactification of $(1,0)$ little string theories of type…

Recently an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi-Yau threefolds has been proposed. At the same time an exact quantization condition for the cluster…