Related papers: BMN Correlators by Loop Equations

We calculate the one-loop QCD corrections for the decay of an off-shell vector boson with vector couplings into two pairs of quarks of equal or unequal flavours keeping all orders in the number of colours. These matrix elements are relevant…

Recently it was established that the one-loop planar dilatation generator of N=4 Super Yang-Mills theory may be identified, in some restricted cases, with the Hamiltonians of various integrable quantum spin chains. In particular Minahan and…

The goal of this paper is to study the BMN correspondence in the fermionic sector. On the field theory side, we compute matrix elements of the dilatation operator in N=4 Super Yang-Mills for BMN operators containing two fermion impurities.…

We study the integrability properties of Wilson loops in the ${\cal N}=6$ three-dimensional Chern-Simons-matter (ABJM) theory. We begin with the construction of an open spin chain that describes the anomalous dimensions of operators…

We propose a nonperturbative framework to study general correlation functions of single-trace operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at large $N$. The basic strategy is to decompose them into fundamental building…

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in…

We study a completely-packed loop model with crossings in a three-dimensional lattice and confirm it is described by $\mathrm{RP}^{n-1}$ sigma field theories. We use Monte Carlo simulations, with systems sizes up to…

We find the eigenvalue of the kernel of BFKL equation in the next-to-next-to-leading logarithm approximation in the planar N=4 SM theory from the constraints, coming from the six-loop anomalous dimension of twist-2 operators and known…

We present a three-loop O(g^6) calculation of the difference between the expectation values of Wilson loops evaluated in N=4 and superconformal N=2 supersymmetric Yang-Mills theory with gauge group SU(N) using dimensional reduction. We find…

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…

We consider a special double scaling limit, recently introduced by two of the authors, combining weak coupling and large imaginary twist, for the $\gamma$-twisted $\mathcal{N}=4$ SYM theory. We also establish the analogous limit for ABJM…

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to $\Gamma(H\to b \bar b)$, to be $c_5=-6900\pm…

The recent work `A unified Bayesian inference framework for generalized linear models' \cite{meng1} shows that the GLM can be solved via iterating between the standard linear module (SLM) (running with standard Bayesian algorithm) and the…

We consider correlation inequalities that follow from the well-known loop equations of LGT, and their analogues in spin systems. They provide a way of bounding long range by short or intermediate range correlations. In several cases the…

We continue the study of n-point correlation functions of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the l-loop corrections…

We consider higher-point generalizations of the "octagon" large-charge four-point function in planar N=4 super Yang-Mills theory. These n-point polygon correlators are defined as ten-dimensional null limits of generating functions of…

A class of exact non-renormalized extremal correlators of half-BPS operators in N=4 SYM, with U(N) gauge group, is shown to satisfy finite factorization equations reminiscent of topological gauge theories. The finite factorization equations…

Mean plausible values can be computed when Bayesian structural equation modeling (BSEM) is performed. As mean plausible values do not preserve the inter-factor correlations, they yield path coefficients that are different from the estimated…

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…

The approximative calculation of iterated nested expectations is a recurring challenging problem in applications. Nested expectations appear, for example, in the numerical approximation of solutions of backward stochastic differential…