Modul: MAT971 Stochastische Prozesse

## CFT on the lattice: Virasoro relations and the critical Ising model

Prof. Dr. Fredrik Viklund talk

**Date:** 22.05.19 **Time:** 17.15 - 19.00 **Room:** Y27H12

Conformal field theory (CFT) is a powerful but non-rigorous approach to describing scaling limits of critical lattice models in the plane. CFT methods have been used to, e.g., predict exact formulas for correlation functions and values for critical exponents. For some models, some of the predictions can now be proved using discrete complex analysis and SLE techniques. A key structure in the CFT approach is the Virasoro algebra, an infinite dimensional Lie algebra. I will report on joint work with Clement Hongler and Kalle Kytölä that uses discrete complex analysis to construct a representation of the Virasoro algebra in terms of lattice fields of the critical Ising model, thereby tightly linking the principal exactly solvable structures for the lattice model and the CFT. Along the way I will also briefly review a corresponding result for the discrete Gaussian free field.