# Light branes and swampland/landscape

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!

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 ~ $\exp(-\alpha.dist)$.
• 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... – riemannium Mar 13 '18 at 21:11
• 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): $\Gamma \sim \exp (-M_P^2/M_{3/2})$. – riemannium Mar 13 '18 at 21:31