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Following a talk by Cumrum Vafa, I understood that light branes are important as he quoted the formula: $$m\sim \exp(-\alpha M/M_P)$$ and then, he stated that light massive particles AND extended objects (particle/p-brane species) are produced as we get $M>M_P$, where $M_P$ is the Planck mass. However, in Cosmology, we are commonly said that masses or arbitrarily number of states are not allowed since they would cause the Universe to collapse. Why light p-branes are not "problematic" for Cosmology? And secondly, is the above formula something related to Schwinger effect in string theory? Where does that formula comes from?

Extra clarification: what motivated my question is the fact that arXiv:1603.04583 shows the rate is, instead the formula by Vafa (I think they are similar but not the same): $\Gamma\sim\exp(-M_P^2/M_{3/2})$

Comment: it also remembers me the Hagedorn transition in string theory, but it is not the same at first sight!

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I cannot find the exact formula above, anywhere. But there are conjectures in which a quantity of the form $\exp(-\alpha.dist)$ appears - where dist is distance in field space (and $\alpha$ is just a parameter).. For example, conjecture 2 in Ooguri Vafa 2006, or the "refined swampland conjecture" of Klaewer Palti 2016.

In these conjectures, one considers two versions of a theory that are "dist" apart - e.g. a scalar field with vev v, or with vev v+dist. The argument is the one that Vafa makes in his talk, at around 40 minutes - that when the field distance is big enough, the new version of the theory must have extra light states of mass ~ $\exp(-\alpha.dist)$.

I haven't really studied these things, but we have already seen, in the "weak gravity conjecture", the argument that if black holes can evaporate completely, certain light particle states must exist. If you can have a vev of over a Planck mass in your field theory, perhaps that implies new types of black holes and therefore the new light particles too.

You ask about cosmological implications. If we consider our universe as described by a particular effective field theory, the new light states will show up only when fields (like the inflaton) take on superplanckian values. So by my understanding, those light states are simply not relevant in the post-inflationary universe.

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  • $\begingroup$ 39:21...Essentially, the fluctuation of a field $M=\Delta \varphi$, over the Planck mass. Indeed, you can turn any field fluctiation into mass in natural units...Above Planck mass...that is a bit confusing but "OK" with Schwinger effect, excepting the fact that you get extended objects if they are too light... $\endgroup$ – riemannium Mar 13 '18 at 21:11
  • $\begingroup$ Indeed, what motivated my question is the fact that arXiv:1603.04583 shows the rate is, instead the formula by Vafa (I think they are similar but not the same): $\Gamma \sim \exp (-M_P^2/M_{3/2})$. $\endgroup$ – riemannium Mar 13 '18 at 21:31
  • $\begingroup$ @riemannium That must be the wrong arxiv number? $\endgroup$ – Mitchell Porter Mar 14 '18 at 0:23

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