Ivan Kostov  研究员学术报告

Title: Solvable discrete model of Sine-Liouville gravity

Speaker: Ivan Kostov

Affiliation: Paris-Saclay University, France（法国巴黎萨克雷大学）

Time: 10:00-11:00, Friday, 8th May, 2026 (UTC+8, Beijing Time)

Venue: Room 1502, Shing-Tung Yau Center, Sipailou Campus of Southeast University（东南大学四牌楼校区丘成桐中心1502室）

Inviter: Yunfeng Jiang（江云峰）

Abstract

The sine-Liouville gravity is discretised as a “dilute" vertex model on a random lattice represented by the ensemble of trivalent planar graphs. The vertex model is characterised by a continuous parameter (temperature) and admits a loop expansion similar to that of the O(n) loop model on a random lattice. However, there is an important distinction: the loop weights are no longer topological and the dynamics of the loops is now entangled with the local geometry of the lattice. The vertex model is solved by mapping to a dual large N matrix model which resembles the simplest (N=1) Nekrasov partition function. The spectral curve of the matrix model is an infinite cover of the two-dimensional torus. The continuum limit, described by sine-Liouville gravity, is the limit where the torus degenerates into a cylinder. The phase structure of sine-Liouville theory extracted from the matrix model resembles that of the sine-Gordon model on a flat lattice. In particular, one observes a gravitational analogue of the massless flow in the sine-Gordon model with purely imaginary mass coupling, studied by Fendley, Saleur and Al. Zamolodchikov in the 90s. The flow relates two c=1 theories of 2D gravity compactified on circles with different radii.

Speaker

Ivan Kostov obtained his PhD in 1982 from the Moscow State University, with scientific advisers Vladimir Feinberg and Alexander Migdal. Then he worked in the group of Ivan Todorov at the INRNE Sofia, and since 1990 as a CNRS researcher at the IPhT, CEA-Saclay, France. Currently he is emeritus DR CNRS at IPhT.

His research interests include random matrix models and two-dimensional quantum gravity, geometrical critical phenomena and random surfaces, conformal field theories, exactly solvable models, integrability in gauge and string theories.