Beijing Institute of Mathematical Sciences and Applications

Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov

Antons Pribitoks

Tuesday, October 15, 2024 4:00 PM - 5:00 PM

A6-101

We prove that the supersymmetric deformed $\mathbb{CP}^1$ sigma model (the generalization of the Fateev-Onofri-Zamolodchikov model) admits an equivalent description as a generalized Gross-Neveu model. This formalism is useful for the study of renormalization properties and pa cheese freerticularly for calculation of the one- and two-loop $\beta$-function. Remarkably we find new Nahm-type conditions, which guarantee renormalizability and supersymmetric invariance. We show that in the UV the superdeformed model flows to the super-Thirring CFT, for which we also develop a superspace approach. It is then demonstrated that the super-Thirring model is equivalent to a sigma model with the cylinder $\mathbb{R}\times S^1$ target space by an explicit computation of the correlation functions on both sides. Apart from that, we observe that the original model has another interesting conformal limit, given by the supercigar model, for which we also find a chiral dual and explicitly demonstrate agreement of the four-point functions on both sides. In addition, we investigate novel relations of our construction through mirror symmetry and dimensional reduction, which in the framework of $\sigma$-models on toric varieties maps to a class of $\mathcal{N}=2$ Liouville (Landau-Ginzburg class), as well as topological theories in higher $D$.