Week 13.02.2022 – 19.02.2022

In this talk, I will review a duality between correlation function and null polygon Wilson loops and present this duality from a conformal bootstrap perspective. In the process I will also work out, in detail, a new duality between spinning three point functions in large N conformal gauge theories and null polygonal hexagonal Wilson loop.

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.

The Standard Model extended with non-renormalisable operators is increasingly becoming THE theory of the elementary particles and their interactions. A large part of current and future research is devoted to test this theory to the best possible accuracy. To this aim, though, substantial knowledge on its quantum structure is needed, both for theoretical reasons (constraints on the basis of relativity+quantum mechanics) and experimental ones (combine data gathered at very different energies). In this talk I will discuss the progress made over the years in this respect, with particular emphasis on major obstacles.