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5d N=1 SCFTs and Gauge Theories on Brane Webs: September 27 – October 1, 2021

Organized by Amihay Hanany, Marcus Sperling, Antoine Bourget and Julius Grimminger

Five dimensional (5d) Lagrangian gauge theories are non-renormalizable, however many 5d N=1 supersymmetric gauge theories can be understood as effective infrared (IR) descriptions of 5d or 6d conformal fixed points in the ultraviolet (UV) under the renormalization group (RG) flow. Consequently, several questions need to be addressed such as:

 – What are all possible 5d and 6d conformal fixed points?
– Under which circumstances is the UV completion a 6d theory? 
– What are all valid IR gauge theories with an existing UV completion? 
– Which IR gauge theories flow from the same conformal fixed point? 
– How do properties like the global symmetry and the Higgs branch of the moduli space change under the RG-flow? 
– What is the set of protected operators of the SCFT and what is their operator product expansion (OPE)? 
– How does the Higgs branch change as one varies mass parameters and Coulomb branch moduli? 
– What is the full moduli space of a 5d N=1 SCFT? How can we describe its singularity structure (Hasse diagram)?

A multitude of techniques to study 5d theories has emerged over the recent years. Amongst them are the superconformal index; techniques of 6d compactifications; Calabi-Yau constructions in F and M theory; combined fibre diagrams; and magnetic quivers.

A very potent realization of 5d N=1 theories, which is linked to those techniques, is given by 5-brane webs in Type IIB superstring theory. This approach has proven vital in questions regarding symmetry enhancement, dualities, as well as constructions of gauge theories with non-classical gauge groups or non-fundamental matter content. This workshop aims to focus on these developments and build new connections between geometric constructions and physical observables in order to expand and chart the landscape of 5d SCFTs.