Related papers: Determinant formula for the octagon form factor in…

We compute the n-point two-loop form factors of the half-BPS operators Tr(phi_{AB}^n) in N=4 super Yang-Mills for arbitrary n >2 using generalised unitarity and symbols. These form factors are minimal in the sense that the n^{th} power of…

We develop analytical methods for computing the structure constant for three heavy operators, starting from the recently proposed hexagon approach. Such a structure constant is a semiclassical object, with the scale set by the inverse…

Some aspects of correlation functions in N=4 SYM are discussed. Using N=4 harmonic superspace we study two and three-point correlation functions which are of contact type and argue that these contact terms will not affect the…

In this talk I discuss the form factor approach used to compute correlation functions of integrable models in two dimensions. The Sinh-Gordon model is our basic example. Using Watson's and the recursive equations satisfied by matrix…

We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for numerical computations whether the basis elements are…

We study correlation functions in the one-dimensional $\mathcal{N}=2$ supersymmetric SYK model. The leading order 4-point correlation functions are computed by summing over ladder diagrams expanded in a suitable basis of conformal…

To each 4x4 matrix of reals another 4x4 matrix is constructed, the so-called associate matrix. This associate matrix is shown to have rank 1 and norm 1 (considered as a 16D vector) if and only if the original matrix is a 4D rotation matrix.…

With the help of strong-coupling theory, we calculate the critical exponents of O(N)-symmetric phi^4-theories in 4- epsilon dimensions up to five loops with an accuracy comparable to that achieved by Borel-type resummation methods.

The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…

We argue that the conventional method to calculate the OPE coefficients in the strong coupling limit for heavy-heavy-light operators in the N=4 Super-Yang-Mills theory has to be modified by integrating the light vertex operator not only…

We study multipoint correlators of protected scalars on the Maldacena-Wilson line in $\mathcal{N}=4$ SYM. Working at weak coupling in the planar limit, we derive an explicit recursion relation that captures next-to-leading order correlators…

We consider a semiclassical (large string tension ~ \lambda^1/2) limit of 4-point correlator of two "heavy" vertex operators with large quantum numbers and two "light" operators. It can be written in a factorized form as a product of two…

We consider general cyclic representations of the 6-vertex Yang-Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov-Stroganov model and the corresponding chiral Potts model on finite size lattices. We first…

Integrated correlator of four superconformal stress-tensor primaries in $SU(N)$ $\mathcal{N}=4$ super Yang-Mills (SYM) theory in the perturbative limit takes a remarkably simple form, where the $L$-loop coefficient is given by a rational…

We consider strong 't Hooft coupling expansion in special four-dimensional $\mathcal N=2$ superconformal models that are planar-equivalent to $\mathcal N=4$ super Yang-Mills theory. Various observables in these models that admit…

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…

The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…

An explicit analytic formula is presented that computes the conformal (super-)block decomposition of any free scalar or half-BPS diagram in 1d, 2d or 4d CFTs, with various supersymmetries, including none. We prove our formula by exploiting…

Rosengren and Schlosser introduced notions of ${\it R}_N$-theta functions for the seven types of irreducible reduced affine root systems, ${\it R}_N={\it A}_{N-1}$, ${\it B}_{N}$, ${\it B}^{\vee}_N$, ${\it C}_{N}$, ${\it C}^{\vee}_N$, ${\it…

We present a general method for analytically factorizing the n-fold form factor integrals $f^{(n)}_{N,N}(t)$ for the correlation functions of the Ising model on the diagonal in terms of the hypergeometric functions…