Holography and the Loewner energy

Date: 2022-08-10

Time: 14:00 - 15:00


Yilin Wang


As a starting point of AdS/CFT correspondence, the link between the hyperbolic geometry of 3-manifolds and the conformal metrics on its boundary has been explored extensively. One basic fact is that Mobius transformations on the Riemann sphere extend to isometries of the hyperbolic 3-space H^3 and they are in one-to-one correspondence. The Loewner energy is a Mobius invariant quantity that measures the roundness of Jordan curves. It arises from large deviation deviations of SLE0+ and is a Kahler potential on the Weil-Petersson Teichmuller space. We show that the Loewner energy equals the renormalized volume of a submanifold of H^3 constructed using the Epstein surfaces associated with the hyperbolic metric on both sides of the curve. This is a work in progress with Martin Bridgeman (Boston College), Ken Bromberg (Utah), and Franco Vargas-Pallete (Yale).