Higher co-dimension de Sitter branes

We extend the arguments of Maldacena and N\'u\~nez to include higher co-dimension brane setups and derive a new no-go theorem. Specifically, we show that under reasonable assumptions on the energy-momentum conservation and the bulk curvature, co-dimension-two branes fail to support stable de Sitter solutions. For co-dimensions higher than two embedded in a compact internal space, we show that negative tension sources would be required. This result places strong constraints on the viability of higher-dimensional braneworld models as a means to obtain de Sitter space within string theory.