Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions.

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.

Operator Product Expansion for Form Factors.

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 nontrivial bootstrap constraints, which are sufficient to fully determine it. We evaluate the form factor transition for maximally helicity-violating form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce operator product expansion predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature.

Rigorous Bounds on the Analytic S Matrix.

We consider a dual S-matrix bootstrap approach in d≥3 space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions.

Derivation of the Holographic Dual of a Planar Conformal Field Theory in 4D.

We present the first-principles derivation of a weak-strong duality between the fishnet theory in four dimensions and a discretized stringlike model living in five dimensions. At strong coupling, the dual description becomes classical and we demonstrate explicitly the classical integrability of the model. We test our results by reproducing the strong coupling limit of the four-point correlator computed before nonperturbatively from the conformal partial wave expansion. Because of the extreme simplicity of our model, it could provide an ideal playground for holography with no supersymmetry. Furthermore, since the fishnet model and N=4 super Yang-Mills theory are continuously linked, our consideration could shed light on the derivation of AdS/CFT for the latter. For simplicity, in this Letter we restrict our considerations to a large subset of all states.

Collinear limit of scattering amplitudes at strong coupling.

In this Letter, we consider the collinear limit of gluon scattering amplitudes in planar N=4 super-Yang-Mills theory at strong coupling. We argue that in this limit scattering amplitudes map into correlators of twist fields in the two dimensional nonlinear O(6) sigma model, similar to those appearing in recent studies of entanglement entropy. We provide evidence for this assertion by combining the intuition springing from the string world-sheet picture and the predictions coming from the operator product expansion series. One of the main implications of these considerations is that scattering amplitudes receive equally important contributions at strong coupling from both the minimal string area and its fluctuations in the sphere.

Spacetime and flux tube S-matrices at finite coupling for N=4 supersymmetric Yang-Mills theory.

We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature.