Dynamical edge modes in p-form gauge theories

Abstract

We extend our recently identified dynamical edge mode boundary condition to p-form gauge theories, revealing their edge modes as Goldstone bosons arising from gauge transformations with support on the boundary. The symplectic conjugates of these edge modes correspond to the electric-field-like components normal to the boundary. We demonstrate that both the symplectic form and the Hamiltonian naturally decompose into bulk and edge parts. When the boundary is a stretched horizon, we show that the thermal edge partition function reduces to that of a codimension-two ghost (p – 1)-form residing on the bifurcation surface. These findings provide a dynamical framework that elucidates observations made by several authors. Additionally, we generalize Donnelly and Wall’s non-dynamical approach to obtain edge partition functions for both massive and massless p-forms. In the context of a de Sitter static patch, these results are consistent with the edge partition functions found by several authors in arbitrary dimensions.