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I should preface this question that I am new to understanding the string landscape and swampland program and F-theory, so I apologize if my question is obvious / unclear!

Recently I was reading some of the literature of SO(10,2) M-Theory extensions, and F-Theory— specifically as “a toolbox” for studying Type2b non-perturbative effects, elliptic fibrations and axio-dilaton, etc. and it being a T-dual description of kk-compactified M-theory (less clear to me but I can grasp this); and came across a general introductory talk on the landscape and swampland by Vafa [https://workshops.ift.uam-csis.es/pgf18, “String Landscape and the Swampland” - Cumrun Vafa]. While all of this was a very trivial introduction (I assume to a more general audience than string researchers), there was one point of the talk I thought I would ask about.

About a half hour into the talk, Vafa references consistent theories without string theory description, and this can be “captured by some principle / motivated” by black hole physics in particular. My first question is, what are some of these consistent theories that do not exist in the string landscape? Where do they have a full description? How do we know, by a matter of principle, this is true? My second is, where is this black hole description of string landscapes further investigated? Is there an original paper / full survey of this relationship? Is this description even defined and known or is it speculated?

My last is more of a stupid question and not related to the talk, but it is not obvious to me. I am aware of the large landscapes of f-theory compactifications on CY4 (~10^272000 I have heard referenced) and those with standard model consistency (10^15), where are these estimates originally made and is there any case where F-theory is able to reduce the vast expanse of the landscape (say more like 10^500)? Are there other methods that are able to reduce the size of the landscape to less than that often cited 10^500?

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  • $\begingroup$ Welcome to PhysicsSE! I have voted to close your question as off-topic for being too broad. Please make sure your post asks a single, well-focused question. It is better to avoid asking multiple questions. $\endgroup$ – BioPhysicist Oct 21 '19 at 1:34
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    $\begingroup$ Your link doesn’t work for me. $\endgroup$ – G. Smith Oct 21 '19 at 5:21
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Vafa indeed believes that all possible consistent quantum theories of gravity are string theories, this was recently elevated to a principle known as The string lamppost principle.

When Vafa says "whithout string theory" when talking about quantum gravity constrains, he refers to "down to top restrictions" or "without including stringy corrections to semi-classical Einstein's gravity", it is to say, the ones that can be seen at the semi-classical level, from the rules of quantum mechanics or those expected on general grounds. Examples are unitarity, absence of remnants, anomaly cancellation, no hair theorems (needed for "no continuous global symmetries" and "no non-trivial cobordism classes in moduli space" swampland criteria), Hawking's formula for the entropy of a black hole (needed for "all charges must appear" criteria), cosmic censorship hypothesis (related to the weak gravity conjecture) etc.

Remarkably, all the above statements are very robust in the context of string theory.

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