John Preskill has tweeted virtually an interesting, soon-to-be-published termination yesteryear Harlow together with Hiroši Ooguri:
Ooguri together with Harlow let on that entanglement wedge reconstruction inward AdS/CFT rules out global symmetry inward the mass gravity theory. #QIQG3 pic.twitter.com/RcVnMc7PJx
— John Preskill (@preskill) August 16, 2017
They appear to brand some lore rigorous.
The lore says that at that spot are no global symmetries inward consistent theories of quantum gravity. In a moral sense, this implication results from the "gravity" business office of "quantum gravity", non from the "quantum" one. Why? Because Einstein's theory of gravity, the full general theory of relativity, makes everything "local". In particular, the beingness of a gravitational champaign depends on what yous are "locally doing".
In a minor lab e.g. Einstein's elevator, the accelerated motion is indistinguishable from the gravitational champaign of a large object. This principle, the equivalence principle, actually agency that yous may imagine the Universe to endure a grid of many labs together with the switch to an accelerating coordinate organisation may endure done independently inward each parent (cell).
Well, I should convey been to a greater extent than clear. What full general relativity is may endure described every bit an extension of the special relativity's symmetry principles. In special relativity, yous may rotate, translate, together with Lorentz boost coordinate systems. In full general relativity, yous may brand the translations unlike at unlike points of the spacetime – which also allows the boosts or whatever nonlinear transformations of the coordinates, too.
So full general relativity says that the stiff Poincaré grouping has to endure extended to the infinite-dimensional diffeomorphism group. It's non difficult to believe that morally speaking, full general relativity also "should" promote all other global symmetries to their local counterparts. Why? Look at the Kaluza-Klein theory. That's a theory inward which the \(U(1)\) or \(G\) approximate grouping becomes geometrically realized every bit an isometry grouping of the compactification manifold – e.g. an extra (fifth) circular dimension of the spacetime. But full general relativity allows the translations inward this periodic coordinate \(x^5\to x^5 + \varepsilon\) to endure spacetime-dependent, i.e. \(\varepsilon=\varepsilon(x^0,x^1,x^2,x^3)\), thence this isometry which could endure a global symmetry inward a non-gravitational theory must teach a local, approximate symmetry, too. (I promise that you're OK amongst my counting, 0,1,2,3,5, which makes things clearer LOL.)
This declaration is but an analogy, although a persuasive one. Symmetries don't convey to endure geometrized inward the Kaluza-Klein way, yous could object. So does the determination agree inward general? Do all global symmetries convey to endure promoted to local ones? You may sure as shooting let on classically consistent theories of gravity amongst global symmetries.
Within some detail superselection sectors or descriptions of some vacua of quantum gravity, this lore may endure proven, however. As the Preskill's photograph of Ooguri's lecture indicates, Ooguri together with Harlow are going to struggle that they convey a proof that a global symmetry inside the AdS infinite would ruin the locality inward the AdS space. At the linguistic level, it sounds plausible: globalists (such every bit George Soros together with the people whom he has bought) fighting against the localists. ;-) However, this "understanding" is imitation – it is by together with large a coincidence that "global symmetries" are incompatible amongst "locality" inward this sense. In spite of the randomness of this "simple to sympathise result", it seems to endure correct together with they convey a proof.
So all the global symmetries that nosotros notice inward the boundary CFT must silent be inward the AdS infinite inward some sense. But the correct feel is that they are together with they convey to endure extended to a local, approximate group. Moreover, Ooguri together with Harlow volition hopefully offering us a clear proof that physical states transforming inward every finite-dimensional irreducible representation of the grouping \(G\) convey to be inward the mass theory.
This is a declaration nosotros would frequently hash out inward the context of the weak gravity conjecture. Once yous create upwards one's hear that the charges must prevarication inward a lattice \(\Gamma\), for example, is it guaranteed that for every lattice site, at that spot exists a physical object/state that has precisely this value of the charges? This declaration is a "strengthening" of the Dirac quantization dominion but this strengthening can't endure proven every bit good easily – the commons proof of the Dirac quantization dominion isn't enough, for example. The minimum magnetic monopoles could endure \(N\) times to a greater extent than charged than the "theoretically minimal" ones, afterward all.
But inward string theory, they ever appear to convey the minimum charges. The representations of \(G\) are a non-Abelian generalization of this lattice discussion. So they should examine that everything that seems to endure allowed must endure allowed, indeed.
There are many relationships to the weak gravity conjecture. Harlow already wrote a related newspaper ii years ago. First, the weak gravity conjecture is a stronger version of the declaration that at that spot are no global symmetries. Why? It's because the weak gravity conjecture bans really minor values of the coupling \(g\) – together with the minor values of \(g\) would permit a approximate symmetry to "mimic" the physical behaviour of a global symmetry arbitrarily accurately, which should endure forbidden every bit well. When yous ban murders, i.e. stabbing of some other soul that is at to the lowest degree 1 inch deep, yous should ameliorate discourage the 0.99 inch stabbings every bit well, shouldn't you? ;-)
Also, I holler back that their proofs could convey amusingly unproblematic together with group-theoretical consequences for some detail vacua, e.g. for the pure AdS three-dimensional gravity which is dual to the monster grouping CFT if the radius is minimal. I've discussed my proposal that Schur's orthogonality relations convey something to do amongst the ER-EPR correspondence. The monstrous AdS/CFT vacuum manifestly uses all 194 irreps of the monster grouping but I believe that they're acting on each other inward some interesting ways together with some nontrivial identities volition endure proven to agree for the monster grouping that follow from physics inward \(AdS_3\). I believe that the monstrous pure gravity vacuum is the exclusively quantum gravity vacuum where the approximate grouping is purely finite together with discrete (massless states are absent etc.) together with this could hateful some special identities obeyed yesteryear this finite grouping that no other grouping obeys.
The dark hole microstates inward this \(AdS_3\) come upwards inward all 194 irreps of the monster group. But because the monster grouping is a local approximate group, every bit Harlow together with Ooguri also appear to prove, "cosmic strings" should endure allowed whose monodromy around them is equal to whatever chemical factor of the monster group. In three-dimensional spacetimes, "cosmic strings" (codimension ii objects inward the spacetime) should endure interpreted every bit zero-dimensional particles. So shouldn't they endure the same objects every bit the microstates inward 194 irreps?
If it's so, the 194-dimensional infinite may convey ii natural bases which are parameterized either every bit conjugacy classes of the monster grouping (by the monodromy); or every bit the irreps. The characters should orbit yous the matrix elements to switch from 1 soil to another. But I don't know what to practice amongst the "other" degrees of liberty that aren't purely group-theoretical.
You could endure surprised that I am maxim that these states convey monodromies around them – but the dark hole microstates are mutually local inward the CFT. Well, that doesn't hateful that they convey to endure mutually local inward the bulk. I believe that a natural "Dirac string" or the branch cutting may endure drawn every bit a line of piece of occupation betwixt the mass object (black hole) together with a dot on the AdS boundary.
I expression the issue of target readers who convey made it to this dot to endure comparable to a dozen thence it's possible that I won't proofread this text.