Tuesday, May 19, 2020

The logical relationship between quantum gravity and extended objects

Aside from the damn time-consuming Bitcoin puzzle (which may be ingenious or stupid, we will see in two days) – something that destroyed 30% of the night between Sunday and Monday for me – I spent hours by thinking about some good old topics, like the relationship between Matrix theory and wormholes, Matrix theory and the black hole complementarity, and more.

I have some biological instincts that want me to share the findings but I have learned enough to see "it is throwing pearls to swine" (dear readers will surely appreciate this assessment) so I won't discuss my advances. If I generously squeeze all my modesty into this sentence, a 22nd century historian decoding some old notebooks sounds like a better audience to me. Let me write about the writings by others instead.

In recent months, many people started to post their semi-technical essays to hep-th. Today's example is
A symmetry principle for emergent spacetime
by Edgar Shaghoulian (Ithaca). I am interested in the nationality of this bizarre name. OK, in his essay written to win some money from an "essay contest" where real physicists often compete with the armchair physicists (and usually lose), he proposes some relationship between quantum gravity (and the emergent spacetime) on one side and the higher-form symmetries on the other side.

You know, in gauge theories, you have the action where \(A_\mu\), the gauge potential, is integrated over the world line of a charged particle, \(e\int dx^\mu A_\mu\). String theory has lots of extended objects (strings and branes), starting with the fundamental strings, which generalize it to \(\rho \int d\Sigma^{\mu\nu...}B_{\mu\nu...}\).

Edgar believes that one may use the Landau paradigm about the phases of matter – and these symmetries are consequences of a broken symmetry (with the higher number of indices) and their order parameter (like in magnetism). I don't quite follow the arguments and can't subscribe to his answers now but I surely find the question important. But it is clear that he believes that the traditional "condensed matter technology" about phase transitions is directly relevant for quantum gravity – although most quantum gravitists probably tend to think that condensed matter physics is much shallower and more squalid.

Well, on one hand, I tend to agree that the extended objects are more or less necessary for the consistency of a quantum gravitational theory, at least in \(d\geq 4\). This may be one of the "swampland principles". In fact, this essential role of extended objects is the most straightforward strategy to prove that a consistent theory of quantum gravity must be string theory. You just first prove that there are extended objects, perhaps the macroscopic ones, then you show that they may also be as small as allowed by the uncertainty principle, and then you show that their low-mass excitations must interact and behave just like string theory predicts, too.

On the other hand, I still tend to think about the generalized \(p\)-form fields and their charged objects (strings as branes) as about "straightforward", almost field-theoretical objects that are much more conventional than the depth of quantum gravity with the emerging spacetime.

A part of this intuition from the previous paragraph boils down to string field theory – it is much easier to formulate string field theory for open strings and open strings are non-gravitational. These string field theories include D-branes as their classical solutions. So these are some rather conventional solutions to a seemingly non-gravitational theory. The theory knows about gravity from the loops but it doesn't explicitly contain gravitons as physical states (or any closed string states).

Yes, string field theory is "more complex" than local quantum field theories of the basic type. At least, we need to generalize those local field theories to theories with infinitely many fields. But I still tend to believe that the generalization is relatively mild: string field theory is "much like" Yang-Mills theory and other non-gravitational theories. There is no information loss paradox, ER-EPR, black hole complementarity here, and other things. At least it looks so. You just extend the number of fields to infinity (to the Hagedorn tower) but many inequalities for the high-energy behavior of scattering amplitudes still hold etc. Open string field theory really saturates some inequality that are natural in non-gravitational field theories.

But it is possible that this reasoning is misleading and even string field theory secretly knows about all the effects of quantum gravity and those effects may be logically identified with the existence of the \(p\)-form gauge fields, the higher-dimensional generalizations of Yang-Mills theory. After all, starting with the AdS/CFT and Matrix theory (but even e.g. the Weak Gravity Conjecture of ours is doing something of the sort – it says that gravity can never be dominant in the ecosystem of forces which probably means that it's also a mistake to identify the "pure quantum gravity" part of a theory with the source of all the deep mysteries), we have learned lots of equivalences between quantum gravitational and non-gravitational theories. The separation may be (or must be?) much less Iron-Curtain-like than I (and others) used to think. Maybe the transition from a non-gravitational to a gravitational theory is just a small step for a woman, a great one for wxmankind. (Note that I am extremely politically correct to name things after the stupider half of mankind, too.)

If someone can reconstruct some properties of quantum gravitational theories from others, especially if he reconstructs "more mysterious gravitational properties" from the "seemingly more mundane non-gravitational traits", it's important and we should try to understand all these ideas as well as possible.

It could be fun and perhaps even useful if all respected enough experts in quantum gravity were forced to write an essay explaining "whether I believe that the gravitational part of a quantum theory of gravity and other forces is more fundamental than the other parts, whether they are separable at all, and how it should affect our understanding and search for a theory of both". There are lots of other questions I would like to be answered by the big shots – so that people may compare where they actually are when it comes to the bigger questions that are nevertheless affected by the people's more down-to-earth and well-defined research.

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