On the Spectrum of the Local $${\mathbb {P}}^2$$ Mirror Curve

Abstract

AbstractWe address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi–Yau threefold called local $${\mathbb {P}}^2$$ P 2 in the case of complex values of Planck’s constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.