Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2018-05

Burkhard Eden, Yunfeng Jiang, Marius de Leeuw, Tim Meier, Dennis le Plat, Alessandro Sfondrini


Positivity of hexagon perturbation theory.


Abstract: The hexagon-form-factor program was proposed as a way to compute three- and higher-point correlation functions in N = 4 super-symmetric Yang-Mills theory and in the dual AdS5×S5 superstring theory, by exploiting the integrability of the theory in the ’t Hooft limit. This approach is reminiscent of the asymptotic Bethe ansatz in that it ap- plies to a large-volume expansion. Finite-volume corrections can be incorporated through Lüscher-like formulae, though the systematics of this expansion are largely unexplored so far. Strikingly, finite-volume corrections may feature negative powers of the ’t Hooft coupling g in the small-g expansion, potentially leading to a breakdown of the formalism. In this work show that the finite-volume perturbation theory for the hexagon is compat- ible with the weak-coupling expansion for arbitrary n-point functions, and is positive on the nose.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2018-05


23 pp.