Boundaries and Defects of N=4 SYM with 4 Supercharges, Part I: Boundary/Junction Conditions

Understand

We consider ${\cal N}=4$ supersymmetric Yang Mills theory on a space with supersymmetry preserving boundary conditions.

• The boundaries preserving half of the 16 supercharges were analyzed and classified in an earlier work by Gaiotto and Witten.
• We extend that analysis to the case with fewer supersymmetries, concentrating mainly on the case preserving one quarter.
• We develop tools necessary to explicitly construct boundary conditions which can be viewed as taking the zero slope limit of a system of D3 branes intersecting and ending on a collection of NS5 and D5 branes oriented to preserve the appropriate number of supersymmetries.