Talk page
Title:
Terminal singularities, Hyperkahler Quotients and Quiver N-ality
Speaker:
Abstract:
In the program of geometric engineering, a very large class of non-Lagrangian 4d $\mathcal{N}=2$ SCFTs are obtained by compactifying Type IIB String Theory on Calabi-Yau three-folds which are singular hypersurfaces in four complex dimensions. Generically, the Higgs branches of such SCFTs are difficult to determine because of non-trivial quantum corrections. However, an appropriate circle reduction of a 4d SCFT may lead to a 3d SCFT with a quiver description, and the resultant quiver then gives a realization of the 4d Higgs branch as a hyperkahler quotient. In this talk, I will present an explicit construction to show that the Higgs branch for a large subclass of these 4d SCFTs admits \textit{more than one} hyperkahler quotient realization. A recently discovered N-ality (i.e. equivalence of N distinct theories) involving three dimensional quiver gauge theories plays a crucial role in the story. I will discuss how the property of 3d N-ality is encoded in the geometry of the CY three-fold used to engineer the 4d SCFT.
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