Type IIB Forms and Scalars from an $\mathrm{SL}(2,\mathbb{R})$ Topological Field Theory with Boundary

Abstract

We formulate the scalar and form-field sector of type IIB supergravity as an eleven-dimensional topological field theory with boundary. Unlike the pseudo-action, it is a genuine action principle with manifest global $\mathrm{SL}(2,\mathbb{R})$ symmetry. The IIB fields arise as edge modes: a boundary term breaks the $\mathrm{SL}(2,\mathbb{R})$ gauge symmetry to $\mathrm{SO}(2)$, so the axion-dilaton parametrizes $\mathrm{SL}(2,\mathbb{R})/\mathrm{SO}(2)$, and the boundary field equations give the duality relations, including $F_5$ self-duality. As the action never refers to the axion-dilaton directly, S-duality monodromies become holonomies of a flat connection.