Mixed Gauge-Global Symmetries, Elliptic Modes, and Black Hole Thermodynamics in Horava-Lifshitz Gravity

Physical theories are largely dictated by their symmetries. One important conjecture in this vein is that a consistent quantum gravity theory may not possess a global symmetry, but rather only local gauge symmetries, a conjecture which has recently been extended to generalized global symmetries. Historically, this conjecture arose from a heuristic argument using black hole thermodynamics and was recently proven to hold in AdS/CFT. In Horava-Lifshitz gravity, a presumed consistent theory of quantum gravity for which there is strong evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is "mixed": it is a local symmetry in one coordinate that remains global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. We show how the corresponding charge, which has previously not been considered thermodynamically, coupled with the other features above, resolves some outstanding tensions. Hence this mixed symmetry is not precluded by horizon thermodynamics, but is instead an integral feature. This expands the types of symmetries in quantum gravity compatible with black hole thermodynamics.