Geometry at Strong coupling for amplitudes/Wilson loops

09/26/2023 11:00 am - 12:00 pm
Daniel Kapek Jue Liu Puskar Mondal
CMSA, 20 Garden St, G10
Website:https://cmsa.fas.harvard.edu
Address: 20 Garden Street, Cambridge, MA 02138 USA

General Relativity Seminar

Speaker: Lionel Mason (Oxford)

Title: Geometry at Strong coupling for amplitudes/Wilson loops

Abstract: The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop computed by Alday & Maldacena in terms of the area of a minimal surface in AdS_5. To do so they developed a `Y-system’ for computing the amplitude. This talk re-interprets their construction as providing the underlying twistor space for a hyperKahler structure on the corresponding space of kinematic data. In particular, the area is given by a Kahler scalar for the pseudo-hyperkahler structure and satisfies a version of the Plebanski equations, a well-known completely integrable system. This geometry encodes the properties of the space of kinematic data on which the amplitude depends as a cluster variety tying into its positive geometry and cluster variety structure. Similar constructures are possible for other cluster varieties corresponding to form factors and beyond.