Supersymmetric boundary conditions in N = 4 super Yang-Mills theory

Davide Gaiotto, Edward Witten

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188 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)789-855
Number of pages67
JournalJournal of Statistical Physics
Volume135
Issue number5-6
DOIs
StatePublished - Jun 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Boundary conditions
  • Quantum field theory

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