It has recently been recognized that various observables in different four-dimensional supersymmetric gauge theories can be computed for an arbitrary 't Hooft coupling as determinants of certain semi-infinite matrices. It turns out that these quantities can be expressed as Fredholm determinants of the so-called Bessel kernel and they are closely related to celebrated Tracy-Widom distribution (more precisely, its finite temperature generalization) describing level-spacing distributions in matrix models. We exploit this relation to determine their dependence on the ’t Hooft coupling constant. Unlike the weak coupling expansion, which has a finite radius of convergence, the strong coupling expansion is factorially divergent, necessitating the inclusion of nonperturbative, exponentially small corrections. We develop a method to systematically compute these corrections and discuss the resurgent properties of the resulting transseries.

I will review a recent progress in computing four-point correlation functions of infinitely heavy half-BPS operators in planar N = 4 SYM. Taking advantage of integrability of the theory, these correlation functions can be constructed in terms of fundamental building blocks - the octagon form factors. We show that the octagon form factor can be expressed as a Fredholm determinant of an integrable Bessel operator and demonstrate that this representation is very efficient in finding its dependence on the ’t Hooft coupling and two cross ratios. At weak coupling, this yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we apply strong Szego limit theorem to develop a systematic expansion of the octagon in the inverse powers of the coupling constant and calculate accompanying expansion coefficients analytically. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

[For zoom link please contact s.nagyATqmul.ac.uk. There will be a pre-seminar for students at 13:30] The energy-energy correlation (EEC) measures the angular distribution of the energy that flows through two calorimeters separated by some relative angle in the final state created by a source. We present a new approach to computing this observable that exploits the relation between the energy correlations and four-point correlation functions of conserved currents. In the limit of small and large angles, when EEC describes the correlation between particles belonging, respectively, to the same jet and to two almost back-to-back jets, we obtain a concise representation of the EEC in terms of the conformal data of twist-two operators and verify it by comparing with the results of explicit calculation at next-to-next-to-leading order in maximally supersymmetric Yang-Mills theory. As a byproduct of our analysis, we predict the maximal weight part of the analogous QCD expression.

I will review a recent progress in computing scattering amplitudes in N=4 SYM theory and explain the recently found duality between MHV gluon scattering amplitudes and correlation functions of half-BPS protected operators in the limit where the positions of the adjacent operators become light-like separated.