BRST-invariant boundary conditions and strong ellipticity

Abstract: The quantisation of gauge theories usually procedes through the introduction of ghost fields and BRST symmetry. In the case of quantum gravity in the presence of boundaries, the BRST-invariant boundary value problem for the gauge field operators is non-elliptic, and consequently the definition of the effective action using heat-kernel techniques becomes problematic. This paper examines general classes of BRST-invariant boundary conditions and presents new boundary conditions for quantum gravity which fix the extrinsic curvature on the boundary and lead to a well-defined effective action. This prompts a discussion of the wider issue of non-ellipticity in BRST-invariant boundary value problems and when the use of gauge-fixing terms on the boundary can resolve the issue.