## Thursday, September 06, 2018

### Building the spacetime from BC-bits

Many new hep-th papers mention the swampland but there have been many texts about these disputed ideas on this blog so let me pick something great and less disputed.

Mark Van Raamsdonk is the main father of the idea to connect pieces of spacetime by the quantum entanglement in the role of the glue – and therefore the forefather of the ER-EPR correspondence, among other things. In his new preprint,
Building up spacetime with quantum entanglement II: It from BC-bit
whose title was chosen as a continuation of a paper from 2010 (over 500 followups now; the second, new part of the title is a variation of Wheelers' "it from bit") – a nice gap for a series – he introduces the BC-bits.

The term "BC-bit" was chosen after Mark agreed with the current government of British Columbia (where he works) that he will promote the province and then he will become the prime minister. Alternatively, in front of physicists, Van Raamsdonk may claim that BC stands for "boundary conformal" because he's using boundary conformal field theories.

Needless to say, lots of approaches to quantum gravity have tried to construct the spacetime out of some "pieces" and most of them are pretty much hopeless – spin networks and spin foams in loop quantum gravity are the most famous example of that category. Instead, in Mark's picture, it's important that the individual pieces are connected by entanglement. Well, to some extent, it is true even in spin networks.

But it's really the internal "beef" of the pieces of the spacetime where Mark makes a genuine contribution. His pictures and maybe ideas look suspiciously similar to my old scheme to perturbatively prove the AdS/CFT correspodence for the maximally supersymmetric gauge theory in four dimensions – see e.g. a discussion of a paper by Berkovits for a similar stuff that is out in the literature.

In my picture, the Feynman diagrams of the gauge theory are interpreted as two-dimensional surfaces (that's of course the good old 't Hooft) divided into faces. The faces are treated as Poincaré disks using the Euclidean AdS2/CFT1 correspondence. So there's some two-dimensional gravity theory living in the two-dimensional faces but that's holographic, so it may be reduced to the physics of the boundary – which happens to be the propagators of the Feynman diagrams.

In that paradigm of mine, I also assumed that the propagators of the Feynman diagrams are the places where the position field $$x^\mu$$ labeling the AdS5 space hits the boundary of the anti de Sitter space.

Well, what Mark has really seems to be the same thing but he avoids the interpretation that it's a proof of AdS/CFT. Instead, he emphasizes it is an example of the entanglement-as-glue paradigm. Using something that looks like LEGO created out of pieces, he is building a "model" of a spacetime claimed to be generic. The two-dimensional faces that make up the map are supposed to be causal diamonds of an AdS spacetime near the boundary. By redrawing such a region using the faces, he may approximate the conditions in the causal diamonds arbitrarily accurately.

In the spin network case, what would live in the faces would be just some Wilson line around the boundary or something like that. However, consistent theories of quantum gravity dictate a more self-sufficient picture. The BC-bits must be full-blown compact spacetimes – examples of AdS/CFT – with all their degrees of freedom. And we may be connecting these BC-bits by the quantum entanglement.