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.

Relative locality: theory of QG must entail relativity of point-coincidences. b/c momentum obeys non-linear composition law a la non-linear SR law of velocity combination.

Asymptotic safety:

GR as QFT non-renormalizable. So might think non-fundamental effective theory.

But Weinberg thinks safety might allow it to be fundamental after all.

Question arises: what is fundamental theory,

Two questions: why guiding principles in qg.

empirical guidance is unavailable.

Why these two? Little on asymptotic safety and relative locality.