Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory

TL;DR

This paper investigates boundary conditions in N=4 super Yang-Mills theory that preserve half of the supersymmetry, exploring their modifications, moduli spaces, and implications for electric-magnetic duality, with a focus on Lorentz-invariant and deformed boundary conditions.

Contribution

It introduces new boundary conditions in N=4 super Yang-Mills theory, analyzes their moduli spaces, and discusses their behavior under electric-magnetic duality, including non-Lorentz-invariant deformations.

Findings

Modified boundary conditions allow scalar fields to have poles at the boundary.

Moduli spaces of solutions to Nahm's equations are explored in the presence of boundaries.

Preliminary insights into electric-magnetic duality actions on boundary conditions are provided.

Abstract

We study boundary conditions in N=4 super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a ``pole'' at the boundary. The obvious Neumann boundary conditions can be modified by coupling to additional fields supported at the boundary. The obvious boundary conditions associated with orientifolds can also be generalized. In preparation for a separate study of how electric-magnetic duality acts on these boundary conditions, we explore moduli spaces of solutions of Nahm's equations that appear in the presence of a boundary. Though our main interest is in boundary conditions that are Lorentz-invariant (to the extent possible in the presence of a boundary), we also explore non-Lorentz-invariant but half-BPS deformations of Neumann boundary conditions. We make preliminary comments on the action of electric-magnetic duality, deferring a more serious study to a later paper.