We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators. ----- Part of the London Integrability Journal Club. If you are a new participant please register at integrability-london.weebly.com. Link emailed on Tuesday.

We propose an operator product expansion for planar form factors of local operators in N = 4 SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their dual description in terms of periodic Wilson loops. A form factor is decomposed into a sequence of known pentagon transitions and a new universal object that we call the “form factor transition”. This transition is subject to a set of non-trivial bootstrap constraints, which allows us to bootstrap it at any value of the coupling. We evaluate the form factor transition for MHV form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce OPE predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature. [for zoom link contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

In the talk I'll consider theories of weakly interacting higher spin particles in flat spacetime. We will focus on the four-point scattering amplitude at high energies and imaginary scattering angles. Both, the leading asymptotic of the amplitude and the first sub-leading correction in this regime turn out to be universal. The leading asymptotic is equal to the corresponding limit of the Veneziano amplitude. We will compute the first sub-leading correction using a model of relativistic strings with massive endpoints and argue that it is unique using holography, the effective theory of long strings and bootstrap techniques.

We study non-planar corrections to gluon scattering amplitudes in N = 4 SYM theory. In this talk, we focus on the first correction. It is computed by the double trace amplitude and is suppressed by one power of 1/Nc with respect to the leading single trace contribution. We extend the duality between planar scattering amplitudes and null polygonal Wilson loops to the double trace amplitude. The new duality allows us to extend the notion of loop integrand beyond the planar limit and to determine it using recursion relation. It also allows us to apply the integrability pentagon approach to the first non-planar order. We shortly discuss higher orders in the 't Hooft 1/Nc expansion.