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We consider the mutual commutativity of Dunkl operators of the rational Calogero model as zero-curvature condition and calculate the non-local operator, related to these flat connections. This operator has physical meaning of particular…
We present new strong-coupling series for O(N) spin models in three dimensions, on the cubic and diamond lattices. We analyze these series to investigate the two-point Green's function G(x) in the critical region of the symmetric phase.…
We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. In the symmetric phase of its global Z_2 symmetry, two colourless…
We propose the zero-point of the cluster-cluster correlation function as a sensitive test for the shape of the power spectrum of initial fluctuations. It is now possible to go beyond the power law description to measure the point at which…
Despite tremendous progress in our understanding of scattering amplitudes in perturbative (super-) gravity, much less is known about other asymptotic observables, such as correlation functions of detector operators. In this paper, we…
We study the correlation functions of scalar operators in the theory defined as the holographic dual of the Schroedinger background with dynamical exponent z=2 at zero temperature and zero chemical potential. We offer a closed expression of…
We find the general solution of the conformal Ward identities for scalar $n$-point functions in momentum space and in general dimension. The solution is given in terms of integrals over $(n-1)$-simplices in momentum space. The $n$ operators…
Consider the minimal renormalizable extension of the Standard Model with purely dimensionless couplings, successful electroweak symmetry breaking (via the Coleman-Weinberg mechanism) and a see-saw mechanism for neutrino mass: we will call…
We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.
We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the…
We extend our previous definition of K-theoretic invariants for operator systems based on hermitian forms to higher K-theoretical invariants. We realize the need for a positive parameter $\delta$ as a measure for the spectral gap of the…
The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain $n$-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method…
We study abstract weakly relevant flows in a general number of dimensions. They arguably provide the simplest example of renormalization group (RG) flows between two non-trivial fixed points. We compute several two-point correlation…
We calculate one- and two-point correlators of winding operators in the matrix model of 2D string theory compactified on a circle, recently proposed for the description of string dynamics on the 2D black hole background.
Building on the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, and by defining the Zeta and related functions including the Hurwitz Zeta function…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
In this article, we will show how to use Zamolodchikov's higher equations of motion in Liouville field theory to explicitly calculate $N$-point correlation numbers in minimal Liouville gravity for $N>4$. We find the explicit expression for…
We study the two-point correlation functions for the zeroes of systems of $SO(n+1)$-invariant Gaussian random polynomials on $\mathbb{RP}^n$ and systems of ${\rm isom}(\mathbb{R}^n)$-invariant Gaussian analytic functions. Our result…
In this paper we provide a step towards the understanding of the O($n$) bulk operator algebra. By using a mixture of analytical and numerical methods, we compute (ratios of) structure constants, and analyse the logarithmic structure of the…
We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete…