Integrable models of directed polymers on the square lattice
Thimothée Thiery (LPT ENS Paris)
Motivated by the aim of gaining a better understanding of the KPZ universality class in 1+1 dimension (KPZUC), there has recently been a strong research activity focused on finding exact solutions of models in the KPZUC. Indeed, interesting properties such as the emergence of Tracy-Widom (TW) type fluctuations in such models have up to now only been understood in integrable models. In this talk I will focus on one class of models believed to be in the KPZUC, namely directed polymers (DP) on the square lattice, and on one technique used to find exact solutions: the coordinate Bethe Ansatz (CBA). After an introduction to the links between KPZ and DP, I will show how one can identify the underlying algebraic structure present in any CBA solvable model of DP, therefore allowing to classify all such models. This classification contains all previously known exactly solvable models of DP on the square lattice as well as a new one, the Inverse-Beta polymer. Finally, I will sketch how CBA solvability permits to show the KPZUC (critical exponents and TW fluctuations) of the Inverse-Beta polymer.