Related papers: Classical Virasoro irregular conformal block

In this short note, we prove a formula for the group inverse of a block matrix and consider the pseudo principal pivot transform expressed in terms of group inverses. Extensions of the usual principal pivot transform, where the usual…

We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index beta=1,2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance…

We obtain Bargmann-Michel-Telegdi equations of motion of classical spinning particle using Lagrangian variational principle with Grassmann variables.

We derive an explicit expression for the $1/c$ contribution to the Virasoro blocks in 2D CFT in the limit of large $c$ with fixed values of the operators' dimensions. We follow the direct approach of orthonormalising, at order $1/c$, the…

Virasoro conformal blocks are a family of important functions defined as power series via the Virasoro algebra. They are a fundamental input to the conformal bootstrap program for 2D conformal field theory (CFT) and are closely related to…

The Lie conformal algebra of loop Virasoro algebra, denoted by $\mathscr{CW}$, is introduced in this paper. Explicitly, $\mathscr{CW}$ is a Lie conformal algebra with $\mathbb{C}[\partial]$-basis $\{L_i\,|\,i\in\mathbb{C}\}$ and…

We study the beta-deformed matrix models using the method of refined topological string theory. The refined holomorphic anomaly equation and boundary conditions near the singular divisors of the underlying geometry fix the refined…

For a nonrelativistic classical particle undergoing arbitrary oscillations, the generalized effective potential Y is derived from nonlinear eigenfrequencies of the particle-field system. Specifically, the ponderomotive potential is extended…

A conformal field theory can be recovered, via the Kontsevich-Miwa transform, as a solution to the Virasoro constraints on the KP tau function. That theory, which we call KM CFT, consists of d \leq 1 matter plus a scalar and a dressing…

We establish the correspondence between the classical and quantum butterfly effects in nonlinear vector mechanics with the broken $O(N)$ symmetry. On one hand, we analytically calculate the out-of-time ordered correlation functions and the…

Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro-Kac-Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS$_3$…

On the space of generic conformal blocks the modular transformation of the underlying surface is realized as a linear integral transformation. We show that the analytic properties of conformal block implied by Zamolodchikov's formula are…

Consider rectangular matrices over a local ring R. In the previous work we have obtained criteria for block-diagonalization of such matrices, i.e. U A V=A_1\oplus A_2, where U,V are invertible matrices over R. In this short note we extend…

A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off…

We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to…

The conformal bootstrap is applied to percolation and dilute self-avoiding polymers, two theories with Virasoro central charge $c=0$ in two dimensions. In both cases we propose a spectrum of operators motivated by Virasoro symmetry which is…

An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical…

We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…

A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…

Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials. Using this presentation we give a generating set in the space of conformal blocks at any level if the marked…