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I Weak gravity conjecture and strings vs loops

  1. Jun 24, 2017 #1
    “If the weak gravity conjecture is right, loop quantum gravity is definitely wrong,” said Nima Arkani-Hamed, a professor at the Institute for Advanced Study who co-discovered the weak gravity conjecture.

    source https://www.quantamagazine.org/where-gravity-is-weak-and-naked-singularities-are-verboten-20170620/

    which also goes into detail weak gravity conjecture, which states that gravity must always be the weakest force in any universe.

    I was of the understanding in certain braneworld scenarios, string theory "predicts" that gravity is the same strength as the other forces, including electromagnetism and strong force, but gravity - gravitons, are closed loops and its strength can be "diluted" by traveling to other higher dimensional branes, whereas electromagnetism and strong force consists of open ended strings suck on our 3-brane

    so string theory "predicts" gravity is the same strength as the other forces, but is diluted as it is the only force consisting of closed strings, but string theory also "predicts" weak gravity conjecture that gravity must always be weaker than the other forces.

    and this somehow disproves loop quantum gravity

    can anyone elaborate?

    why in string theory can't there be a universe whereby gravity and the other forces have the same strength, and other where gravity is the stronger force, and any combination in between

    why does Nima Arkani-Hamed say weak gravity conjecture if true disproves loop quantum gravity when string theory predicts that in some universes gravity is the same strength as the other forces, but in others, it is weaker?
  2. jcsd
  3. Jun 25, 2017 #2
    I believe the weak gravity conjecture comes from thinking about elementary particles and micro black holes. For example, there has been some discussion of whether an electron could be a micro black hole. However, the repulsion due to its charge is always stronger than the attraction due to its mass, so there is no distance at which gravitational attraction overpowers electromagnetic repulsion, no gravitational "point of no return", no event horizon, and so it is not a black hole.

    This is an example of the sense in which "gravity is the weakest force" - of the fundamental forces exerted by the electron, the electromagnetic force is stronger than the gravitational force. One meaning of the weak gravity conjecture, is that this is true for all elementary entities (including soliton-like objects like monopoles). The motivating idea is that there should be no stable micro black holes - micro black holes should always be able to decay further, into objects that aren't black holes.

    This comes from thinking about the interplay between black hole entropy and the possible gauge field charges of a black hole - if there could be stable charged micro black holes, they would come in too many possible masses to be consistent with the black hole entropy formula. I haven't gone through the reasoning myself, but I can see that this is what it's all about.

    So: it's thought that any theory which successfully combines general relativity and quantum field theory, will contain black holes obeying the space-time thermodynamics figured out by Bekenstein and Hawking, because they deduced it through very general arguments, rather than by assuming a specific theory of everything. And it's now also thought that quantum gravity cannot coexist with an extremely weak gauge interaction, because it would imply too many black hole microstates to be consistent with the Bekenstein-Hawking entropy formula.

    String theory seems to be consistent with the entropy formula, and it also seems to be consistent with the weak gravity conjecture. Arkani-Hamed is saying that loop quantum gravity is not consistent with the weak gravity conjecture, because the electromagnetic coupling can be made as weak as you want. Smolin says, maybe it can't. I will care about that debate, when loop quantum gravity produces a model that can actually describe interactions of gravitons, photons, and charged matter.

    You mention the Randall-Sundrum model, as a string theory model in which gravity is strong. Randall-Sundrum has two braneworlds, and gravity is stronger on one than on the other, because of their relative positions in a warped fifth dimension. I think the idea must be that gravity on the four-dimensional brane is weakened by a leakage of graviton wavefunction into the fifth dimension, and that there is a greater fifth-dimensional volume around the brane with weak gravity.

    In any case, the paper which introduced the weak gravity conjecture addresses something like this scenario when it discusses a "Planck brane" (top of page 8). Then some other branes are introduced, and a version of the weak gravity inequality (equation 13) is deduced, that must apply to massive W-boson-like strings that are attached to these probe branes. They argue that in this example, what matters is the size of the five remaining dimensions, and that they cannot find a way to reduce their volume, while simultaneously maintaining the warp radius, that would violate the conjecture.

    The aspect of the weak gravity conjecture that is of most interest to me, is mentioned in the abstract, and again on page 3: "extrapolating the Standard Model to high energies, there must be new scale Λ beneath the Planck scale with Λ ∼√αGUT/GN ∼1017 GeV"... since I am interested in scenarios where the standard model is valid to high energies, and the Higgs boson mass is determined by some sort of critical boundary condition, at the energy scale where the standard model as effective theory, must give way to a new theory that includes gravity.

    This deduction of a new scale beneath the Planck scale might be problematic for asymptotic safety, but then asymptotic safety is already believed to be inconsistent with the black hole thermodynamics that motivate the weak gravity conjecture in the first place. However, if some other mechanism to produce a critical Higgs can be found, then it shouldn't matter if it comes into play just one or two orders of magnitude away from the Planck scale; which could also be the scale where larger symmetries like supersymmetry or grand unification are broken.
  4. Jun 25, 2017 #3
    string theory seems to be consistent with BOTH weak gravity conjecture AND gravity is same strength, or even stronger, than the other forces, but its strength is spread out over multiple dimensions

    what would be the implications to string theory if there are stable micro black holes, and they are in fact, dark matter
  5. Jun 25, 2017 #4


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    As usual your premise is wildly incorrect, so it makes everything difficult to answer. You are badly mixing up very different technical concepts that don't have any obvious connections and likely have come because you have misinterpreted some abstract of a paper that you didn't read properly. Orange + Apple doesn't tell you anything about lemon...

    The weak gravity conjecture is very interesting and is about a constraint of nature that is invisible to the naive effective field theorist, it involves statements about the maximal size of coupling constants undergoing renormalization flow. If those words don't mean anything to you, please consider going back and learning the basics.
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