Does the graviton have to exist?

[Jim Kata]

The graviton is the helicity two particle one gets when quantizing gravity in a metric formulation. There are two reasons why I have this question.

1.) If you formulate gravity in a tetrad formulation you don't seem to have a helicity two particle just the tetrad and the connection which both transform like 1 forms. Also, the tetrad formulation is the one that couples most naturally to matter.

2.) If Ads / CFT is true (which I believe it is), the CFT doesn't have a helicity two particle, and if I understand the meaning of duality correctly the Ads side should be describable in terms of the CFT.

To ask this a different way. What role does the type IIB string theory (which always has a graviton) have on the CFT side. Is there a need for quantum gravity on the Ads side? Could the CFT just generate classical Ads space on the other side of the duality?

Physicist Jonathan Oppenheim questions whether quantum gravity even exists.

I am sure I am not understanding what is going on, and hopefully someone here can elucidate it for me.

 

[Demystifier]

Tetrad and metric formulations of (classical) gravity are equivalent, aren't they? If you have a tetrad, then you also have a metric. Explicitly $g_{\mu\nu}=\eta_{ab} e^{a}_{\mu} e^{b}_{\nu}$.

 

[mitchell porter]

About AdS/CFT: It works as follows.

In ordinary perturbative QFT, you study asymptotic scattering processes, in which particles enter in various directions "from infinity", interact in a superposition of Feynman diagrams, and then exit "to infinity", again in various directions.

If you imagine yourself floating in three-dimensional space, such a scattering process starts with wavefronts coming at you from various directions in the "sky" (the celestial sphere), and ends with wavefronts moving away from you in various directions.

The holographic description is one in which the scattering probabilities (amplitudes) are obtained solely in terms of variables on the celestial sphere. So you specify the directions from which the particles arrived and departed, and you specify the particle species involved, but you never talk about the particles "leaving the surface" of the celestial sphere.

Instead, you define a quantum field theory that only exists on the celestial sphere, not within it. That theory is going to have its own fields phi, psi... And the particles in three dimensions, correspond to particular gauge-invariant combinations of these 2d celestial fields, e.g. Tr(phi(x0)^3), where x0 is some point on the celestial sphere, corresponds holographically to the emission of a particular particle from the direction of x0, into 3d space.

And then the original 3d scattering, is represented in the 2d celestial CFT, as a correlation function between the localized composite operators, that correspond to particles arriving from infinity and particles departing to infinity. You can imagine some kind of superposition of ripples in the sky, corresponding, like the shadows on Plato's cave wall, to the interaction of particles in the three dimensions that you inhabit.

I've tried to give a verbal picture of this. Basically Feynman diagrams within a sphere, corresponding to correlation functions on the surface of the sphere. I don't know how clear it is.

What I've described is the research program of "celestial holography", which is trying to realize holographic duality in ordinary flat space. That hasn't been accomplished, in the sense that the CFTs dual to flat-space physics haven't been identified.

But the program has been carried through for AdS space. So, scattering within AdS space, is posited to be equivalent to correlation functions in a specific CFT defined on the boundary of the AdS space. Each particle species in AdS, corresponds to a particular combination of field operators from the boundary CFT. And for the AdS graviton, it's easy to remember: a graviton corresponds to the stress-energy tensor of the CFT.

The CFT stress-energy tensor, at a particular point on the boundary, is holographically equivalent to the emission of a graviton into the emergent AdS space from that point (emergent from the perspective of the CFT). The scattering of several gravitons within AdS, corresponds to the correlation of CFT stress-energy tensors at multiple points on the AdS boundary. Other particles correspond to other composite operators of the CFT. And that's it.

 

[haushofer]

I like the question: the tetrad is a one-form, smelling like a spin-1 particle. But in gauge theories you look at how fields couple to the conserved charges. Here the metric couples to the stress-energy tensor, and representation theory dictates that this metric field should have spin-2.

To answer your TT-question: the graviton doesn't need to exist as a fundamental particle. It could also "exist" as a quasi-particle, like a phonon. Personally, I think this is more probable. I interpret Hawking and Bekenstein's derivation of black hole entropy as GR's description of spacetime being some statistical approximation to a more fundamental theory. In that sense I suspect that quantizing spacetime directly is akin to quantizing vibrational modes in a lattice.

 

[Jim Kata]

Thank you everyone for your thoughtful responses. I would like to drill down on something Mitchell Porter said: "The CFT stress-energy tensor, at a particular point on the boundary, is holographically equivalent to the emission of a graviton into the emergent AdS space from that point (emergent from the perspective of the CFT)"

The existence of the stress-energy tensor is the best argument for the existence of the graviton. To paraphrase something Weinberg says in volume 1 of his QFT series, to incorporate long-range interactions it is necessary to couple a field to a conserved current. Since we know that the stress-energy tensor is a conserved current, the field coupled to it would be the helicity two graviton.

Back to Mitchell Porter's quote about the emergence of the graviton on the Ads side. Is it known how this works explicitly? Skimming Maldacena's original paper he says: "Since N = 4 d = 4 U(N) SYM is a unitary theory we conclude that, for large N, it includes in its Hilbert space the states of type IIB supergravity on AdS5 X S5. In particular, the theory contains gravitons propagating on AdS5 X S5." How does this work? How does large U(N) enlarge the Hilbert space of N=4 SYM to include the spectrum of IIB supergravity?

 

[mitchell porter]

Skimming Maldacena's original paper he says: "Since N = 4 d = 4 U(N) SYM is a unitary theory we conclude that, for large N, it includes in its Hilbert space the states of type IIB supergravity on AdS5 X S5. In particular, the theory contains gravitons propagating on AdS5 X S5." How does this work? How does large U(N) enlarge the Hilbert space of N=4 SYM to include the spectrum of IIB supergravity?

The quantum states of N=4 SYM can be reinterpreted as quantum states of the IIB theory.

Recall that the CFT (in this case super-Yang-Mills) is defined on the boundary of AdS. I've already mentioned that the IIB spectrum will be constructed by composite SYM operators (i.e. appropriate combinations of SYM field operators). The remaining challenge is construct the AdS space itself.

Here Plato's cave again helps explain. Suppose you have a fire that is used to cast shadows on a wall. If an object is held close to the wall, its shadow will be scarcely bigger than it is. But if it is far from the wall, it will cast an enormous shadow.

The construction of AdS5 space from the boundary, is like reconstructing the object from its shadow on the wall. Suppose there is a particle "Phi" in the IIB spectrum, which corresponds to a composite operator "O_Phi" in SYM. To obtain "Phi" at a given distance from the boundary, we smear the operator "O_Phi" over a region of the d=4 space in which SYM is defined. The larger the region over which you smear the operator, the further from the boundary, and the deeper into AdS5 space, the particle is located.

(There's a lot more than this. E.g. the location of "Phi" in the S5 directions of AdS5 x S5 is built up from vevs of SYM scalars. And large U(N) is needed for IIB supergravity because large U(N) makes the S5 radius large enough that the IIB strings can be approximated as particles in 10 dimensions. For small S5 radius, you probably get some tangle of "long strings"... But for a certain regime of the AdS/CFT correspondence, the mappings I described make sense.)

 

[ohwilleke]

Serious and promising efforts have been made to formulate non-quantum gravity without a graviton, in a theoretically consistent way that can be reconciled with quantum physics. See, e.g., a December 4, 2023 article in Physics magazine, a publication of the American Physical Society (citing peer reviewed published research).

If anything, the balance of the very limited observational evidence slightly disfavors vanilla quantum gravity with a spin-2 massless graviton relative to a non-quantum theory of gravity.

One of the lesser known but important generic phenomenological consequences of a quantum gravity theories with gravitons is that they should induce decoherence in other quanta such photons, neutrinos, and other particles in cosmic rays that pass through gravitational fields (which, of course, everything does to some degree) to a calculable extent. Observational evidence is starting to reach a point where this effect should be possible to detect. But, so far, this effect has not been observed. See, e.g., this July 25, 2023 preprint from IceCube.