So now we have relative locality and asymptotic safety connected to the CM approach to quantum gravity.

Relation to condensed matter approach: CM systems may have analogues to the physics of relative locality.

Both CM versions encode aspect of EFTs in aspects of parameter space topology. Can be related to p-space curvature.

First version: (1) encode low-energy dynamics  in p-space. (2) Stability of low-energy dynamics. (3) Relate topological invariant to p-space curvature.

Second version: (1) encode internal order of condensate in ground state degeneracy (GSD). (2) Demonstrate stability of GSD. (3) Relate GSD to p-space curvature.

Moving on to relative locality: (Amelino-Camelia et al. 2011)

Idea: due to curvature of momentum space. Can see this by comparing the phase spaces of special relativity and GR . Momentum space flat. But for theories with relative locality momentum space curved. Suggestion is that this should happen in QG, because perhaps of non-commutative geometry. Also corrections to relativistic particle dynamics.

Suppose this: EFT and high-energy theory may not need to be related by approximation, but rather emergence. Then perhaps consistent to claim that an AST can emerge in the form of an EFT of a fundamental condensate.

One route: via failure of law-like deducibility (novelty); with ontological distinctness; and ontological dependence. (micro-physicalism from second two)

Questions from Huggett about how QCD and GR can share a UV fixed point. Butterfield concurs. Bain agrees there’s an issue here.

Claim: EFTs in in both versions of CM approach should aspire to be ASTs.

So aspire toward two fixed points: IR for “high energy” condensate. UV fixed point associated with QCD/GR sector.

But may not be consistent to consider an EFT as an AST.

For AST = fundamental theory to all orders. EFT = theory restricted to a gvien energy scale, beyond which new physics arises.

Asymptotic safety: QG must scale towards UV fixed point with a finite number of UV-irrelevant coupling. I.e. decreases toward high energy (fixed point).

finite # of UV-irrelevant couplings.

infinite # of UV-relevant couplings.

Goal of Condensed Matter approach: 

construct EFT that mimics GR and Standard Model

Version A: spontaneous broken symmetries and universality. E.g. Volovik model.

Version B: characterized instead by “topological order”. E.g. Zhang and Hu: 4-d fractional quantum Hall Fluid (FQH).

Vary in the kinds of order that are relevant.

Condensed matter approach to QG:

Mode decomposition of action, integrate out high energy modes, absorb changes into redefined parameters. If successful, find a fixed point for these transformations.

Can stop just at integrating out of high energy modes. This corresponds to EFT.

Relevant to condensed matter bc topological invariants play role both there and in relative locality considerations.