Andrea Raimondo - Affine Gaudin Bethe Ansatz and the ODE/IM correspondence

Abstract: We consider the monodromy-free opers corresponding to solutions of the Affine Gaudin Bethe Ansatz equations. We define and study the spectral determinants (called Q functions) for these opers. We conjecture that the Q-functions obtained from the Affine Gaudin Bethe Ansatz coincide with the Q-functions of the Bazhanov-Lukyanov-Zamolodchikov opers with the monster potential, which are related to the quantum KdV flows according to the ODE/IM correspondence. We give supporting evidence for this conjecture.