Boundary Causality Violating Metrics in Holography

by Sergio Hernandez Cuenca (UCSB)

Thursday 21 Oct 2021, 16:00 → 18:00 Europe/Zurich

In holography, we say that a bulk geometry violates boundary causality if it causally connects boundary points which would otherwise be causally unrelated with respect to the boundary metric. This notion is often discussed in a semiclassical limit, where we expect violations of boundary causality to be genuinely 'bad', leaving us with two options:
1) Use energy conditions to ensure saddlepoints preserve boundary causality via Gao-Wald-like results.
2) Use saddlepoint violations of boundary causality to rule out unphysical theories.
None of these options is available beyond semiclassical physics in quantum gravity; the full bulk path integral includes metrics which violate boundary causality. We are thus faced with a puzzle: How does the bulk gravitational path integral manage to respect a property of its dual theory as basic as boundary causality?

In this talk, I will sharpen this puzzle using boundary microcausality (namely, that local operators at spacelike-separated boundary points must commute). I will then proceed to resolve it by carefully examining boundary conditions in the gravitational path integral. The resolution involves timefolds, which I will show save the day for suitable generalizations of both the extrapolate and differentiate operator dictionaries. This will shed some light on nonperturbative aspects of holography and motivate further explorations. The talk will be based on 2103.05014.