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Consider the usual derivation of Hawking radiation, using quantum field theory (QFT) in the spacetime of a collapsing star. At late times, long after the event horizon has formed, Hawking radiation is independent of the details of the collapse that formed the event horizon. This independence famously leads to the information loss paradox. However, it still depends on which QFT we use. For example, if we use a QFT that doesn't have any spin-$1$ particles in flat spacetime, then the Hawking radiation won't contain any spin-$1$ particles, either.

According to the landscape concept, string theory has lots of different "vacua" — lots of different possible low-energy effective theories. Since the particle content of Hawking radiation can be derived using the low-energy effective QFT, it must also depend on which point we choose in the string-theory landscape when Hawking radiation is derived using string theory.

Is this right? I'm no string theory expert, but I had the impression that black holes in string theory were excellent scramblers, taking whatever goes in and scrambling it beyond practical recognition (even if the information is still recoverable in principle). But the preceding argument seems to say that the scrambling abilities of a black hole are limited: they can't scramble different points in the landscape with each other. Is this right?

Or can black holes mix different points in the landscape, too? If so, then where are the flaw(s) in my reasoning?

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    $\begingroup$ I'm unsure what "scrambling points in the string theory landscape" is supposed to mean here - the points in the landscape are choices for the structure of spacetime as our 4d world times a CY manifold + choices of certain flux cycles, i.e. they are a "global" state of the universe. A black hole is a local phenomenon in (and itself part of !) this spacetime - how is it supposed to "scramble" the overall geometrical structure of spacetime? $\endgroup$ – ACuriousMind♦ Dec 23 '20 at 23:03
  • $\begingroup$ @ACuriousMind That's a good point, and that's exactly the kind of thing I wasn't sure about. I don't have a clear picture of the landscape idea, in particular of how "global" the state is that corresponds to a point in the landscape. Since spacetime is emergent in string theory anyway, except maybe for prescribed asymptotic conditions, and since black holes mess with the smooth-spacetime-manifold model (holographic principle), I was vaguely thinking that maybe black holes can also mess with where we are in the landscape. Not a well-formed thought. $\endgroup$ – Chiral Anomaly Dec 24 '20 at 2:10
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    $\begingroup$ “Scrambling points of landscape” is the property not of black hole but of de Sitter horizons within the context of eternal inflation: an observer cannot know what vacuum lies outside his horizon. $\endgroup$ – A.V.S. Dec 24 '20 at 6:00
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Your third paragraph is correct. Both the entropy, and the Hawking radiation (if supersymmetry is broken) of a stringy Calabi-Yau black hole depend on the details of the effective low energy theory. It is also plausible that the full black hole partition of a black hole, actually depends on all moduli (vector and hyper multiplets) of the background in which a particular black hole solution is found. See section 7.4 in Black Hole Attractors and the Topological String and Holomorphic anomalies in topological field theories for details in the case of a $\mathcal{N}=2$ solution in four dimensions.

I don't fully catch what the phrase "scrambling of points in the string theory landscape" really means. Being a fast scrambler means (in the terminology of Fast scramblers) that a thermodynamical system with some fixed values of its thermodynamical potentials termalize faster that any other system with the same values of its state variables. Because of that, I don't understand what your definition of a "scrambler of points in the string landscape" is.

But if you was asking about the possibility of producing changes on the black hole partition function by means of changing the values of the outside background moduli; the answer is that it is actually possible. As I said, the black hole partition function depends on the background moduli, and perhaps even depends non-perturbatively on all moduli. So, the black hole has a "physical response" for any change of the moduli background; reciprocally, it is in principle possible to change the values of the background by doing quantum operations on the black hole . If the latter response "is faster" than any other "response" of a similar system, seems to be an ambiguous and ill posed question.

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    $\begingroup$ I don't know what my definition of "scrambling points in the landscape" is, either. It was just a vague thought based on my ignorance of what it really means to choose a vacuum in a theory (string theory) where spacetime as we know it is an emergent phenomenon. Thank you for the guidance, and for the reminder that even the entropy of a BH depends on the effective low energy theory. I'm embarrassed that I forgot that basic point, but I suppose forgetting basic points is a common human mistake when we're struggling to learn something new. Thanks! $\endgroup$ – Chiral Anomaly Dec 24 '20 at 15:19
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    $\begingroup$ @ChiralAnomaly Thank you so much for accepting the answer, I'm really glad about the opportunity to serve you. What is at the core of your question is the an effort to try to understand what a choice of vacua means in string theory. That's one of the most mysterious aspects of string theory, we know very little about the dynamical processes involved in the of choice of vacua (because our lack of understand of how a stringy quantum cosmology really looks like), the topology (connectivity) of the landscape. It's pretty interesting to think on that. $\endgroup$ – Ramiro Hum-Sah Dec 27 '20 at 20:51
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    $\begingroup$ @ChiralAnomaly If you are interested in excellent and divulgative texts on the string theory explanation of the black hole entropy, I recommend Conceptual Analysis of Black Hole Entropy in String Theory and Emergence and Correspondence for String Theory Black Holes. Thanks again. $\endgroup$ – Ramiro Hum-Sah Dec 27 '20 at 20:53

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