Related papers: Correlators in two rainbow tensor and complex mult…
In rainbow tensor models, which generalize rectangular complex matrix model (RCM) and possess a huge gauge symmetry $U(N_1)\times\ldots\times U(N_r)$, we introduce a new sub-basis in the linear space of gauge invariant operators, which is a…
We compute three-point functions for the $SL(2,\mathbb R)$-WZNW model. After reviewing the case of the two-point correlator, we compute spectral flow preserving and nonpreserving correlation functions in the space-time picture involving…
We give a refinement of the Kronecker-Hurwitz class number relation, based on a tesselation of the Euclidean plane into semi-infinite triangles labeled by $PSL_2(\mathbb{Z})$ that may be of independent interest.
We consider two level $k$ WZNW models coupled to each other through a generalized Thirring-like current-current interaction. It is shown that in the large $k$ limit, this interacting system can be presented as a two-parameter perturbation…
Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…
We extend the old formalism of cut-and-join operators in the theory of Hurwitz $\tau$-functions to description of a wide family of KP-integrable {\it skew} Hurwitz $\tau$-functions, which include, in particular, the newly discovered…
This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component…
We study extremal and integrated correlators of half-BPS operators in four-dimensional $\mathcal{N}=2$ SQCD and $\mathcal{N}=4$ SYM with $SU(3)$ gauge group. We focus on the large R-charge sector where the number of operators insertions…
We study correlation functions of single-cycle chiral operators in the symmetric product orbifold of N supersymmetric four-tori. Correlators of twist operators are evaluated on covering surfaces, generally of different genera, where fields…
In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…
We calculate correlation functions in matrix models modified by trace-squared terms. First we study scaling operators in modified one-matrix models and find that their correlation functions satisfy modified Virasoro constraints. Then we…
Let $G$ be a connected multigraph with $n$ vertices, and suppose $G$ has been edge-colored with $n-1$ colors so that each color class induces a spanning tree. Rota's Basis Conjecture for graphic matroids posits that one can find $n-1$…
Over the past decades, coordination languages have emerged for the specification and implementation of interaction protocols for communicating software components. This class of languages includes Reo, a platform for compositional…
Boundary correlators of elementary fields in some 2d conformal field theories defined on AdS$_2$ have a particularly simple structure. For example, the correlators of the Liouville scalar happen to be the same as the correlators of the…
This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an important tool to solve the problem of directly counting the number…
String backgrounds associated with gauged $G/H$ WZNW models generically depend on $\alpha'$ or $1/k$. The exact expressions for the corresponding metric $G_{\m\n}$, antisymmetric tensor $B_{\m\n}$, and dilaton $\phi$ can be obtained by…
The Hanbury-Brown Twiss correlation function for two identical particles is studied for systems with cylindrical symmetry. Its shape for small values of the relative momentum is derived in a model independent way. In addition to the usual…
This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
We analyse the correlation functions of $\mathrm{U}(N)$-tensor models (or complex tensor models), which turn out to be classified by boundary graphs, and use the Ward-Takahashi identity and the graph calculus developed in [Commun. Math.…