Boundaries and defects of N = 4 $$ \mathcal{N}=4 $$ SYM with 4 supercharges. Part I: Boundary/junction conditions

Abstract

Abstract:We consider 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.

Boundaries and defects of N = 4 $$ \mathcal{N}=4 $$ SYM with 4 supercharges. Part II: Brane constructions and 3d N = 2 $$ \mathcal{N}=2 $$ field theories

“…In [1], we performed a study of interface conditions for N = 4 super-Yang-Mills theory, and explicitly constructed UV Lagrangians for such defect systems. These defect systems realize 3d N = 2 field theories in the IR, and can be constructed from type IIB brane configurations with D3-branes (which support the 4d N = 4 theory) suspended between 5-brane defects.…”

“…The moduli spaces in question can be identified with the solution spaces of a generalization of Nahm's monopole equations (a dimensional reduction of the Donaldson-Uhlenbeck-Yau equations) with a certain set of boundary conditions which were described explicitly in [1].…”

“…We will then write down the generalized BPS equations following our previous paper [1] (section 2.3), and comment on technical (but important) issues of gauge symmetry breaking and stability in the rest of this section.…”

“…We consider two allowed types of NS5 brane which we call NS5 and NS5 , and two types of D5 brane, which we call D5 and D5 [4,8]. 1 Our convention for orienting the branes is as follows. In general, D3-branes suspended between NS5-type branes contribute 3d vector multiplets while D5-branes intersecting D3-branes contribute quarks.…”

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Abstract:We study the vacuum moduli spaces of 3d N = 2 supersymmetric quantum field theories by applying the formalism developed in our previous paper [1]. The 3d theories can be realized by branes in type IIB string theory, which in a decoupling limit reduce to 4d N = 4 super-Yang-Mills theory on an interval with BPS defects inserted.

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