Magnetic Domains

Abstract

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.

42 pages, minor improvements, published version

References in corpus (44)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Dielectric-Branes
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• On Foundation of the Generalized Nambu Mechanics
• Introduction to sh Lie algebras for physicists
• Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
• Branes, Superpotentials and Superconformal Fixed Points
• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Three-Algebras and N=6 Chern-Simons Gauge Theories
• The M2-M5 Brane System and a Generalized Nahm's Equation
• D-branes, Monopoles and Nahm Equations
• The Noncommutative Bion Core
• Selfdual strings and loop space Nahm equations
• The Self-Dual String Soliton
• A Massive Study of M2-brane Proposals
• On M5-branes in N=6 Membrane Action
• Three Dimensional Gauge Theories and Monopoles
• Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory
• The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory
• M5 from M2
• Categorified Symplectic Geometry and the Classical String
• Nahm Equations and Boundary Conditions
• M2-M5 Systems in N=6 Chern-Simons Theory
• String field theory and brane superpotentials
• Moduli Spaces of Instantons on the Taub-NUT Space
• Multi-monopoles and Magnetic Bags
• Moduli of Monopole Walls and Amoebas
• Harmonic functions, central quadrics, and twistor theory
• M-brane Models from Non-Abelian Gerbes
• Monopoles in AdS
• A Monopole Wall
• Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians
• Constructing Self-Dual Strings
• Monopole Planets and Galaxies
• BPS Magnetic Monopole Bags
• Periodic Monopoles
• Super Yang-Mills Theory with Impurity Walls and Instanton Moduli Spaces
• Dynamics of Periodic Monopoles
• Sheets of BPS Monopoles and Instantons with Arbitrary Simple Gauge Group
• Constructing Generalized Self-Dual Strings
• The large N limit of the Nahm transform
• Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
• Numerical Investigation of Monopole Chains

Cited by in corpus (5)

• BPS Soliton Solutions of a D3-brane Action
• Dynamics of monopole walls
• Instanton Bags, High Density Holographic QCD and Chiral Symmetry Restoration
• Integrability of BPS equations in ABJM theory
• Magnetic bag like solutions to the SU(2) monopole equations on R^3