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

TL;DR

This paper extends the classification of boundary conditions in N=4 supersymmetric Yang-Mills theory to cases with one quarter of the supersymmetry, developing tools to explicitly construct and analyze these boundary conditions via brane configurations.

Contribution

It introduces a systematic approach to construct and analyze boundary conditions preserving one quarter of supersymmetry in N=4 SYM, using generalized Nahm's equations and brane setups.

Findings

Boundary conditions preserving one quarter of supersymmetry are explicitly constructed.

Certain bulk degrees of freedom are lifted by boundary conditions.

Tools for analyzing boundary constraints in supersymmetric gauge theories are developed.

Abstract

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. 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.