Charges and fluxes in Maxwell theory on compact manifolds with boundary

Abstract

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincaré-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.

28 pages, plain TeX

References in corpus (8)

• Self-Duality, Ramond-Ramond Fields, and K-Theory
• Overview Of K-Theory Applied To Strings
• D-brane charge, flux quantisation and relative (co)homology
• Spin and abelian electromagnetic duality on four-manifolds
• The Dirac quantisation condition for fluxes on four-manifolds
• Large Gauge Transformations in M-theory
• Charge and the topology of spacetime
• Abelian Duality and Abelian Wilson Loops

Cited by in corpus (5)

• The integral equations of Yang-Mills and its gauge invariant conserved charges
• Gauge and Integrable Theories in Loop Spaces
• Abelian gauge theories on compact manifolds and the Gribov ambiguity
• Flux quantization in dilatonic Taub-NUT dyons
• Torsion cycles as non-local magnetic sources in non-orientable spaces