Geometry and Physics Seminar

Opers for higher states of quantum KdV models

Sala 6.2.33, FCUL, Lisboa

Por Davide Masoero (Grupo de Física Matemática da Universidade de Lisboa).

Abstract: Let g be an untwisted affine Kac-Moody algebra, and consider the g-valued quantum KdV model, obtained from the quantization of the second Poisson bracket for the Drinfeld-Sokolov construction. The eigenvalues of the Q-operators for the quantum system satisfy the Bethe Ansatz equations. The ODE/IM correspondence affirms that at each state of the quantum model, solutions of the Bethe Ansatz equations can be obtained from a certain opers with values in Lg, the Langlands dual Lie algebra of g. At the ground state this was shown in the sl2 case by Dorey and Tateo and in full generality (i.e. for every simple Lie algebra g) in D. Masoero et al. (Comm Math Phys 2016, 2017).  For higher states only the sl2 case was available, with the appropriate opers being obtained by Bazhanov, Lukyanov and Zamolodchikov. In this talk, I will show how - following a recent insight by Frenkel and Hernandez - one can explicitly construct opers for the higher states of g-valued quantum kdV, for every simply laced affine Kac-Moody algebra g. The talk is based on the joint work with Andrea Raimondo available at arXiv.1812.00228.

GFMUL - Grupo de Física Matemática da Universidade de Lisboa