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

Abstract

We consider $\mathcal{N}=4$ 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. We analyze how these boundary conditions constrain the bulk degrees of freedom and enumerate the unconstrained degrees of freedom from the boundary/defect field theory point of view. The key ingredients used in the analysis are a generalized version of Nahm's equations and the explicit boundary/interface conditions for the NS5-like and D5-like impurities and boundaries, which we construct and describe in detail. Some bulk degrees of freedom suggested by the naive brane diagram considerations are lifted.

75 pages, 21 figures

References in corpus (4)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Interface Yang-Mills, Supersymmetry, and Janus
• Boundaries and Defects of N=4 SYM with 4 Supercharges, Part II: Brane Constructions and 3d N=2 Field Theories

Cited by in corpus (9)

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• Boundaries and Defects of N=4 SYM with 4 Supercharges, Part II: Brane Constructions and 3d N=2 Field Theories
• Four dimensional superconformal theories from M5 branes
• Intersecting Branes, Domain Walls and Superpotentials in 3d Gauge Theories
• Two-dimensional superconformal field theories from Riemann surfaces with boundary
• Solitons on intersecting 3-branes
• Instantons on Calabi-Yau and hyper-Kähler cones