Holographic Action for the Self-Dual Field

Abstract

We revisit the construction of self-dual field theory in 4l+2 dimensions using Chern-Simons theory in 4l+3 dimensions, building on the work of Witten. Careful quantization of the Chern-Simons theory reveals all the topological subtleties associated with the self-dual partition function, including the generalization of the choice of spin structure needed to define the theory. We write the partition function for arbitrary torsion background charge, and in the presence of sources. We show how this approach leads to the formulation of an action principle for the self-dual field.

75 pages; 18 figures; LaTeX

References in corpus (3)

• On the partition sum of the NS five-brane
• Classification of abelian spin Chern-Simons theories
• K-Theory in Quantum Field Theory

Cited by in corpus (7)

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• BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D=6 and M5-branes
• Fivebrane instantons and Calabi-Yau fourfolds with flux
• Type II Actions from 11-Dimensional Chern-Simons Theories
• The Spectra of Supersymmetric States in String Theory
• Gravitational interpretation of the Hitchin equations