*A gravitino ball. Click the image for a video.*

The swampland program deepens our understanding of quantum gravity by refining the conjectures stating that most of the seemingly consistent effective field theories have subtle bugs that prevent them from being completed to consistent theories of quantum gravity i.e. to string/M-theory vacua.

Gravitinos – the supersymmetric partners of gravitons – have entered several swampland hypotheses. For example, exactly one month ago, a paper said that gravitinos mustn't be motionless. Now, in a fresh hep-th Madrid-French-German-Venezuelan paper

Castellano, Font, Herraez and – last but surely not least – Ibáñez ;-) say that the gravitinos can't be too light, or at least they can't be adjusted to be light without additional consequences.A Gravitino Distance Conjecture

In realistic \(\NNN=1\) string vacua, a light gravitino of mass \(m_{3/2}\) (here, 3/2 is the spin of the gravitino) imply that a whole Hagedorn-like tower of massive particles must exist as well which must also be light. The latter doesn't have to be as light as the gravitino itself but the mass scale of the tower obeys \[ M_{\rm tower} \approx m_{3/2}^\delta, \quad \frac 13 \leq \delta \leq 1. \] For an interesting example, if there is a collider-scale gravitino of mass close to \(1\TeV\), then there must be a tower of new particles that start at some intermediate \(10^5-10^{10}\TeV\).

On top of that, the Hubble constant determining the rate of expansion during the inflationary epoch must be rather low if the gravitino is light:\[ H \leq m_{3/2}^\delta M_{P}^{1-\delta} \] Again, it is some geometric average between the gravitino mass and the Planck mass. Isn't it exactly the same scale as \(M_{\rm tower}\)? That would mean that the inflationary epoch must be described along with the whole tower, wouldn't it?

At any rate, as expected from viable swampland papers, they accumulate evidence of various kinds in favor of their statement. An interesting fact is that their gravitino conjecture may be considered a strengthened (because it implies) the AdS distance conjecture.

I am sympathetic towards this proposal because gravitinos are "very quantum" from some perspectives. Well, one must be careful. Gravitons themselves are bosonic quanta of the metric field and they like to make Bose-Einstein condensates which simply change the background metric and that has a nice classical description – or a description in quantized effective field theories.

Due to supersymmetry, gravitinos must also exist and their properties must be pegged to those of the gravitons by supersymmetry. So they look rather classical, too. However, classical fermionic fields must be equal to zero – there are no nonzero anticommuting (fermionic) \(c\)-numbers. Nevertheless, gravitinos apparently can "do things", like produce condensates or perhaps bound states. These physical phenomena come with a mass scale that is also low if the gravitinos are light. If you think about a hydrogen-like bound state and its condensate, it is very obvious that you need the full quantum theory to study it, and these bound states may develop Bose-Einstein condensates as well. Any reduction to "the metric field only" must break down. You just need a tower.

Here, I only talked about the hydrogen-like bound states because they are very well-known ideas. I don't actually believe that it is the best way to think about the new unavoidable phenomena – but maybe even these things do exist. But there should be some new light portion of the spectrum and dynamics.

I don't quite get why the vacua with \(m_{3/2}\)=0 and unbroken supersymmetry don't immediately falsify the conjecture because the conjecture seems to predict a massless tower. Do I misunderstand something?

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