2D sigma models on noncompact Calabi-Yau manifolds and Liouville theory

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2025. Vol. 111. No. 10. Article 106003.

Gavrilenko P., Evgenii Ievlev, Marshakov A., Монастырский И. И., Alexei Yung

We consider a class of two dimensional conformal N = 2 supersymmetric U(1) gauge linear sigma
models with N fields of charges +1 and N fields of charges −1, whose Higgs branches are noncompact toric
Calabi-Yau manifolds of complex dimension 2N − 1. We show, starting from large-N approximation, that
the Coulomb branch of these models, which opens up at strong coupling, is described by N = 2 Liouville
theory and then extrapolate it to exact equivalence demanding the central charge of the Liouville theory to be
c=2N − 1. Next, we concentrate on mostly physically attractive N = 2 and N ≥ 3 cases and find there a
perfect agreement of the set of complex moduli on the Calabi-Yau side with the marginal deformations in
N =2 Liouville theory, supporting proposed exact equivalence.

Keywords: string theory, gauge theories, supersymmetry, Sigma Models, vortices