# Universality and quantum gravity

Here is apparently a quote by Jacques Distler from his blog https://golem.ph.utexas.edu/~distler/blog/archives/000612.html:

“I started off by recounting the tale of Howard Georgi, back in 1982, warning me off studying quantum gravity, as a waste of time. The point is that there’s no decoupling regime in which quantum “pure gravity” effects are important, while other particle interactions can be neglected. “Universality” in field theory — usually our friend — is, here, our enemy. Unless we know all particle physics interactions all the way from accessible energy up to the Planck scale, we can never hope to extract any quantitative predictions about quantum gravitational effects."

Could someone explain what does that statement mean, and if it is true/false? My understanding is that even for non-renormalizable field theories, one can construct effective field theory perturbation expansion. It just happens that at high energy enough, that effective field theory perturbation breaks down but we have perfectly predictive effects of quantum gravity at low energies.

• Jacques' footnote on your paragraph took you halfway there. Ask yourself: How do you switch off gravity in the UV limit? In the IR, you switch off all interactions except for EM, but then you have classical, not quantum theories of neutral assemblies. Nov 6, 2021 at 23:51
• Sorry is there a QFT book chapter you recommend to understand these type of decoupling arguments? I completely miss the physical picture here. We know that the gravity couples only weakly to the stress tensor in the IR. We know it's not renormalizable, so it blows up in the UV, but we're not pretending we understand all the way to the UV anyways. So it's the same problem as any other effective field theory with a non-renormalizable term. I fail to see the distinction. Nov 7, 2021 at 2:46
• Sorry, I meant: how do you switch off all other interactions but gravity in the UV, so as to isolate its telltale effects? Nov 7, 2021 at 2:53
• I don't think it's possible. But why does not having a regime where pure quantum gravity matters is important to do effective field theory? We can capture the leading terms which distort the theory at high energy without caring what it does in the UV. Nov 7, 2021 at 3:11
• Ok, how do you check this distortion, swamped by the other interactions, then? Nov 7, 2021 at 3:14

Like you said, we can include gravity perturbatively in the framework of low-energy effective QFT, as reviewed in reference 1. This works because gravity is extremely weak at the energies that characterize modern particle-physics experiments. But the interest in quantum gravity revolves around nonperturbative/high-energy/strong-field issues, like the holographic principle and the informaion-loss paradox, both of which were already known in the 1970s (references 2,3,4) and were surely on Distler's mind in 1982.

Thanks to universality, very different theories can become indistinguishable from each other at sufficiently low resolution. Low-energy experiments can only fix the first several terms in the lagrangian on which perturbation theory is based. That's what allows us to include gravity in the Standard Model in the sense of low-energy effective theory (reference 1), and I'm guessing this was also the basis for Georgi's assertion. Terms of higher order in the cutoff are not resolved, so we cannot attack the interesting questions about quantum gravity — which are nonperturbative/high-energy/strong-field — by extrapolating upward from the low-energy effective theory.

Even if it was fair at the time, Georgi's "waste of time" judgement is obsolete now, because now we have approaches to studying quantum gravity that don't rely on extrapolating upward from a low-energy effective theory. Perturbative string theory is tightly constrained by numerous anomaly cancellation requirements, which are nonperturbative. Fully nonperturbative formulations like AdS/CFT are also available. (See references 5 and 6 for perspectives about the situation in the more realistic case of asymptotically de Sitter spacetime, which is not understood as well yet.) In hindsight, Georgi/Distler's statement

...there’s no decoupling regime in which quantum “pure gravity” effects are important, while other particle interactions can be neglected

seems to be true in an even stronger sense in string theory. Here's an excerpt from section 2.2 in reference 7:

Typically, the mass scale associated to [quantum gravity] physics is [the Planck mass] $$M_p$$, and one might expect that working at energy scales far below the Planck mass would mean that we lose sensitivity to such physics. But the conjecture says that if in the bulk of moduli space... the tower of states has a mass scale around the Planck mass $$M_p$$ ..., then at large field expectation values this mass scale is exponentially lower than $$M_p$$. Therefore, it claims that the naive application of decoupling in effective quantum field theory breaks down at an exponentially lower energy scale than expected whenever a field develops a large expectation value.

Whether this "stringy" phenomenon is our enemy or our friend, it at least corroborates the idea that the interesting questions about quantum gravity are not things we can study properly by decoupling it from everything else.

1. Donoghue (1995), Introduction to the Effective Field Theory Description of Gravity (https://arxiv.org/abs/gr-qc/9512024)

2. Bekenstein (1973), Black holes and entropy, Physical Review D 7, 2333-2346

3. Hawking (1975), Particle creation by black holes (https://projecteuclid.org/euclid.cmp/1103899181)

4. Hawking (1976), Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460–2473

5. Witten (2001), Quantum Gravity In De Sitter Space (https://arxiv.org/abs/hep-th/0106109)

6. Banks (2010), Supersymmetry Breaking and the Cosmological Constant (https://arxiv.org/abs/1402.0828)

7. Palti (2019), The Swampland: Introduction and Review (https://arxiv.org/abs/1903.06239)

• Thanks a lot for the comment. I understand the insensitivity of the IR physics (things you can measure) on the UV theory thanks to the "irrelevance" of the einstein hilbert action. However this is true for any non-renormalizable theory (4 fermi etc...) so it seems georgi's comment is not specific to gravity. Nov 11, 2021 at 20:21
• @physicsdude You're welcome! And you're right that it's true more generally. But for other interactions, we can observe significant quantum effects at currently accessible energies. For gravity, we can't, because it's far too weak. We know how to calculate scattering amplitudes involving gravitons in low-energy effective field theory, but the calculation itself confirms that the effect is too weak to observe at low energies. Nov 12, 2021 at 2:43