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

Preprint 2020-02

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


Multi-particle finite-volume effects for hexagon tessellations. 




Abstract: Correlation functions of gauge-invariant composite operators in N = 4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting res- olutions of the identity involving virtual (“mirror”) magnons. We consider this problem for five-point functions of protected operators. At one-loop in the ’t Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2019-05


45 pp.