In the last decade there has been great progress in the study of strongly interacting quantum field theories, mainly due to gauge-gravity dualities which relate conformal field theories to string theories in higher dimensional curved backgrounds. More in particular, the discovery of integrability for N=4 supersymmetric Yang-Mills (SYM) gives hope that this theory can be solved exactly in the planar limit. This would give great insights into non-perturbative features of real-world theories such as QCD, since they are closely related in some particular limits.
Being a conformal field theory, N=4 SYM has a convergent operator product expansion, which means that only two sets of numbers need to be understood in order to solve the theory: the spectrum of operators and their structure constants. The first has been solved in the past decade due to the discovery of an infinite amount of extra symmetry, while the latter is the subject of current research. Recently, a conjecture to compute structure constants at any value of the coupling has been proposed, and the prescription consists of a two-point function of twist operators: the Hexagon form factors.
The aim of this project (collaboration with Raul Pereira and Alessandro Georgoudis from Uppsala University and Vasco Gonçalves from ICTP-SAIFR Sao Paulo and Dmitri Chicherin from Mainz University) is to obtain the integrand for the correlation function of 4 protected operators to 5loops. This object is not known and can be used to extract information about the structure constant of the theory. In order to extract the information we need we have to match integrability data, coming from hexagons computations, with pure feynman integrals computation. Part of the computation for the feynman integrals needed were performed by par of the authors (arxiv:1802.00803).
In order to finalize such computation for the 5 loop integrand we needs to use Integration By Parts tools such as LiteRed (arXiv:1310.1145) and FIRE (arXiv:1408.2372 to reduce further Integrals to a basis of simpler integrals in order to obtain further constraints on the integrand.