Holographic Action for the Self-Dual Field

TL;DR

This paper develops a holographic approach to self-dual field theory in higher dimensions, clarifying topological aspects and formulating an action principle through Chern-Simons theory.

Contribution

It introduces a new holographic construction of the self-dual field using Chern-Simons theory, addressing topological subtleties and generalizing the partition function.

Findings

Revealed topological subtleties in self-dual partition functions.

Formulated an action principle for self-dual fields.

Extended the theory to arbitrary torsion backgrounds and sources.

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.