Causality in Holographic Approaches to Quantum Gravity

The development of holographic approaches to quantum gravity introduces a new ingredient into the longstanding question of which metrics should be included in a Lorentzian gravitational path integral. In the most well developed example, quantum gravity with asymptotically anti-de Sitter boundary conditions is equivalent to a quantum field theory (QFT) living on the boundary at infinity. The QFT must be causal with respect to the boundary metric, but there are bulk metrics that violate boundary causality. In other words, two spacelike separated boundary points can nevertheless be timelike related with respect to some bulk metrics. Must these "boundary causality violating" metrics be excluded from the Lorentzian gravitational path integral? I will show that the answer is no: these metrics can be included and still keep the QFT causal.