Symplectic singularities, Phase diagrams, and Magnetic Quivers

Over the past 10 years we faced an impressive progress in the understanding of theories with 8 supercharges. This was through the introduction of theoretical tools which help analyze hypermultiplet moduli spaces in a whole host of gauge theories. Coulomb branches of 3d N=4 theories are now computed very easily through the so called “monopole formula”. The resulting moduli spaces are symplectic singularities which are characterized into different families — closures of nilpotent orbits, intersections of Slodowy slices, orbifolds, slices in the affine Grassmanian, and more. All these names should henceforth enter the physics vocabulary in studies of theories with 8 supercharges.

 

The phase diagrams of symplectic singularities give a further characterization. They are computed with the help of combinatorial tools such as quiver subtraction. This helps distinguish simple/complicated moduli spaces and extends the notion of the Higgs mechanism to theories that admit no Lagrangians.

 

A major ingredient in the success of the recent progress is the use of brane systems for theories with 8 supercharges. Magnetic quivers are computed using these brane systems, and solve long standing problems in finding Higgs branches in regimes where Lagrangian techniques are not available. This sheds light on tensionless strings in 6d, massless instantons in 5d and Argyres Douglas theories in 4d.

 

The talk aims to review the progress in understanding theories with 8 supercharges and to give a taste to the new tools and to the new terminology that rose as a result of this study.