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

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.