## Density matrices in quantum gravity

Tarek Anous, Jorrit Kruthoff, Raghu Mahajan

SciPost Phys. 9, 045 (2020) · published 5 October 2020

- doi: 10.21468/SciPostPhys.9.4.045
- Submissions/Reports

### Abstract

We study density matrices in quantum gravity, focusing on topology change. We argue that the inclusion of bra-ket wormholes in the gravity path integral is not a free choice, but is dictated by the specification of a global state in the multi-universe Hilbert space. Specifically, the Hartle-Hawking (HH) state does not contain bra-ket wormholes. It has recently been pointed out that bra-ket wormholes are needed to avoid potential bags-of-gold and strong subadditivity paradoxes, suggesting a problem with the HH state. Nevertheless, in regimes with a single large connected universe, approximate bra-ket wormholes can emerge by tracing over the unobserved universes. More drastic possibilities are that the HH state is non-perturbatively gauge equivalent to a state with bra-ket wormholes, or that the third-quantized Hilbert space is one-dimensional. Along the way we draw some helpful lessons from the well-known relation between worldline gravity and Klein-Gordon theory. In particular, the commutativity of boundary-creating operators, which is necessary for constructing the alpha states and having a dual ensemble interpretation, is subtle. For instance, in the worldline gravity example, the Klein-Gordon field operators do not commute at timelike separation.

### Cited by 31

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Tarek Anous, -
^{2}Jorrit Kruthoff, -
^{3}Raghu Mahajan

^{1}Institute of Physics, University of Amsterdam [IoP, UvA]^{2}Stanford University [SU]^{3}Institute for Advanced Study [IAS]