Duality and Fluxes in the Sen Formulation of Self-Dual Fields

TL;DR

This paper explores the duality and flux dependence in Sen's formulation of self-dual fields, analyzing partition functions and Wilson surface operators to understand their physical implications.

Contribution

It demonstrates how electromagnetic duality related to the unphysical form influences the partition function and flux dependence in Sen's self-dual field formulation.

Findings

Duality induces a T-like symmetry in the partition function.

Partition function depends on flux choices of the unphysical form.

Two-point functions of Wilson surfaces are explicitly computed.

Abstract

In Sen's formulation of self-dual fields one finds two closed forms: $H^{(g)}$ and $H^{(s)}$. Only the former couples to sources and the spacetime metric. The latter has the wrong sign kinetic term but decouples and hence might be regarded as an unphysical artifact. In this letter we illustrate how an electromagnetic duality associated to the potential for $H^{(s)}$ gives rise to a T-like duality in the partition function for $H^{(g)}$. We then compute the partition function on a (4k+2)-dimensional torus highlighting its dependence on the choice of flux of $H^{(s)}$. Lastly we compute the two-point function of Wilson Surface operators.