Geometry at Strong coupling for amplitudes/Wilson loops

CMSA EVENTS: CMSA GENERAL RELATIVITY SEMINAR

When: September 26, 2023
11:00 am - 12:00 pm
Where: CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138, United States
Speaker: Lionel Mason - Oxford
 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.