Speaker:	Mitch Weaver (KAIST)
Title:	Reading between Special Kähler Structures: N =4 sYM
Date (JST):	Tue, May 20, 2025, 13:30 - 15:30
Place:	Seminar Room A
Abstract:	Quantum field theories (QFTs) possess both local data, e.g.the spectrum and OPEs of local operators, and global data. Global data determines the topologically non-trivial anifolds the theory can be placed on, and the distinct sets of such data define the global variants of the QFT, all of which contain the same local data. For gauge theories, global variants are described by the spectra of genuine Wilson-’t Hooft line operators, but it is natural to ask what field theory data characterizes the global variants of the theory when it doesn’t possess a weakly coupled Lagrangian description. We analyze this question for the moduli space of vacua of a supersymmetric quantum field theory (SQFT) which is an important observable that is known to encode some local data, e.g. the OPEs/chiral rings of BPS operators and BPS spectra. We focus on 4d N =2 superconformal field theories (SCFTs) since they are conjectured to always possess a space of vacua with a Coulomb branch (CB) component whose geometry is described in terms of a special Kähler structure (SKS). When equipped with N =4 supersymmetry, the CB geometry is defined by a (compact) semi-simple Lie algebra, and for simple Lie algebras we classify all possible inequivalent SKSs. We compare these results with the gauge theory analysis of the inequivalent global variants of the analogous 4d N =4 sYM theories under S-duality. For simply laced cases the SKS distinguishes between all global variants, while for non-simply laced cases it is a slightly coarser invariant, failing to distinguish between triples of theories in one S-duality orbit of global structures. Our results suggest that the global variants of 4d N =2 SCFTs can often be determined by, and possibly defined by, the SKSs of their CB geometries.

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