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

Gavrylenko P. Ievlev E. Marshakov A. Monastyrskii I. Yung A.
15 May 2025 American Physical Society

Physical Review D
2025 #111 Issue 10

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.

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International School for Advanced Studies (SISSA), TS, Trieste, 34136, Italy
National Research Center, Kurchatov Institute, Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg, 188300, Russian Federation
Physics Department and Energetic Cosmos Laboratory, Nazarbayev University, Astana, 010000, Kazakhstan
Theoretical and Nuclear Physics Department, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Igor Krichever Center for Advanced Studies, Skoltech, Moscow, 121205, Russian Federation
Department of Mathematics, HSE University, Moscow, 119048, Russian Federation
Higher School of Economics, National Research University, Saint Petersburg, 194100, Russian Federation
Theory Department of LPI, Moscow, 119991, Russian Federation

International School for Advanced Studies (SISSA)
National Research Center
Physics Department and Energetic Cosmos Laboratory
Theoretical and Nuclear Physics Department
Igor Krichever Center for Advanced Studies
Department of Mathematics
Higher School of Economics
Theory Department of LPI

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