Related papers: Classical Liouville Three-point Functions from Rie…
We explore how to compute, classically at strong coupling, correlation functions of local operators corresponding to classical spinning string states. The picture we obtain is of `fattened' Witten diagrams, the evaluation of which turns out…
We present an approach that gives rigorous construction of a class of crossing invariant functions in $c=1$ CFTs from the weakly invariant distributions on the moduli space $\mathcal M_{0,4}^{SL(2,\mathbb{C})}$ of $SL(2,\mathbb{C})$ flat…
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $\mathbb{R}$, we define fractional operators by means of a functional calculus…
We study zero temperature correlation functions of the spin-$1\over 2$ Heisenberg XXZ model in the critical regime $-1< \Delta\leq 1$ in a magnetic field by means of the {\tenit Dual Field Approach}. We show for one particular example how…
We investigate the analogues of certain classical estimates of Littlewood for the Riemann zeta-function in the context of quadratic Dirichlet $L$-functions over function fields. In some situations, we are actually able to establish finer…
It is shown that the general 3-point function $<\Phi_{a} \Phi_{b} \Phi_{c}>$, with continuous values of charges $a, b, c$ of a statistical model operators, and the 3-point function of the Liouville model, could all be obtained by successive…
In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the…
We study the holographic dual of two-point correlation functions for nonconformal field theories. We first take into account a Lifshitz geometry as the dual of a Lifshitz field theory which may appear at a critical or IR fixed point. We…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
While all the cosmological observations are carried out on a light-cone, the null hypersurface of an observer at z=0, the clustering statistics has been properly defined only on the constant-time hypersurface. We develop a theoretical…
The computation of the two-point correlation form factor K(t) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We study the AdS/CFT correspondence with a brane extending in AdS, a setup which is dual to CFT in the presence of a defect. We focus on the correlation function of two local operators and the defect, which is the simplest observable with…
Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we compute the three-point function of a scalar field in a Coleman-De Luccia instanton background. We first compute the three-point function of the scalar field…
We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS$_3\times {\cal N}$ with NS-NS flux and a single-trace $T\bar{T}$ deformation of the symmetric orbifold CFT. We present a…
One of the most important problems in any conformal field theory is the calculation of three-point functions of primary operators. In this paper we provide explicit examples of correlators with two scalar operators in $\,{\cal N}=4$…
In a series of recent papers, a special kind of AdS$_2$/CFT$_1$ duality was observed: the boundary correlators of elementary fields that appear in the Lagrangian of a 2d conformal theory in rigid AdS$_2$ background are the same as the…
We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of…
The three-point current correlation function in Euclidean spacetime for a strongly coupled system with non-Abelian global symmetry, $\langle J^a_i(x)J^b_j(y)J^c_k(z)\rangle$, is calculated from the weakly coupled AdS dual. The contribution…
We examine three point functions with two scalar operators and a higher spin current in 2d W_N minimal model to the next non-trivial order in 1/N expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and 1/N…