Related papers: Factorized Combinations of Virasoro Characters
We present a unified framework for the holographic computation of Virasoro conformal blocks at large central charge. In particular, we provide bulk constructions that correctly reproduce all semiclassical Virasoro blocks that are known…
Fermionic expressions for all minimal model Virasoro characters $\chi^{p, p'}_{r, s}$ are stated and proved. Each such expression is a sum of terms of fundamental fermionic form type. In most cases, all these terms are written down using…
Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface. We introduce a new concept of matrix factorizations for complete intersections that allows us to…
The countably infinite number of Virasoro representations of the logarithmic minimal model LM(p,p') can be reorganized into a finite number of W-representations with respect to the extended Virasoro algebra symmetry W. Using a lattice…
We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the…
With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully…
Nonunique factorization in cancellative commutative semigroups is often studied using combinatorial factorization invariants, which assign to each semigroup element a quantity determined by the factorization structure. For numerical…
We study the category of matrix factorizations for an isolated hypersurface singularity. We compute the canonical bilinear form on the Hochschild homology of this category. We find explicit expressions for the Chern character and the…
Using a summation formula due to Burge, and a combinatorial identity between partition pairs, we obtain an infinite tree of q-polynomial identities for the Virasoro characters \chi^{p, p'}_{r, s}, dependent on two finite size parameters M…
We obtain new fermionic sum representations for the Virasoro characters of the confromal field theory describing the ferromagnetic three-state Potts spin chain. These arise from the fermionic quasi-particle excitations derived from the…
Lambda-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we…
The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new…
We present a brief summary of the recent discovery of direct tensorial analogue of characters. We distinguish three degrees of generalization: (1) $c$-number Kronecker characters made with the help of symmetric group characters and…
We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p,p') minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the…
We enumerate generalizations of the superintegrability property $<character>\ \sim {\rm character}$ and illuminate possible general structures behind them. We collect variations of original formulas available up to date and emphasize the…
We study Virasoro minimal-model 4-point conformal blocks on the sphere and 0-point conformal blocks on the torus (the Virasoro characters), as solutions of Zamolodchikov-type recursion relations. In particular, we study the singularities…
We address prediction problems on tabular categorical data, where each instance is defined by multiple categorical attributes, each taking values from a finite set. These attributes are often referred to as fields, and their categorical…
Rational conformal field theories in 2d have partition functions built from holomorphic characters, whose classification can be addressed via the holomorphic modular bootstrap. This is facilitated by a special basis of ``quasi-characters''…
We study a family of inhomogeneous Ising chain models along with an equivalent family of nearest neighbour particle systems. By the correspondence between the two families we prove identities of combinatorial significance relating to…
The distribution of the characteristic polynomial $Z(U,\theta)$ of $N\times N$ matrices $U$ in the Circular Unitary Ensemble is studied by the method of second quantization for one-dimensional fermions. For infinite $N$ the Gaussian…