## Monday, March 22, 2021

### Gravitino must never be motionless? A swampland hypothesis

In a new hep-th paper
The Gravitino Swampland Conjecture
Edward W. Kolb, Andrew J. Long, and Evan McDonough (Chicago/Houston) propose a new swampland principle – a new condition that must be obeyed for an effective field theory coupled to gravity to be capable of a consistent completion to a regime of quantum gravity and/or string theory. They postulate a simple rule:
The gravitino speed must never drop to zero in any vacuum and any conditions.
If true, such an assumption also has consequences.

We have basically observed elementary particles with the spin 0 (Higgs), 1/2 (leptons and quarks), 1 (photon, gauge bosons), and 2 (graviton, although only in the classical limit of gravitational waves). From the interval 0 to 2 and the spacing of 1/2, the number 3/2 is missing. It is the spin of the gravitino, a superpartner of the graviton, and most people who do quantum gravity would agree with me that it is more likely than not that such a particle with a mass much lower than the Planck mass exists in Nature around us.

These authors justify the claim that the gravitino speed mustn't ever vanish by a simple comment: if it vanished, it would mean that it would be easy to excite modes with an arbitrarily high momentum, and that is why the effective field theory would break down. Well, I think that the justifications of the swampland conditions should be more diverse and multi-dimensional.

Also, I think that this particular reasoning isn't quite a clear example of how the normal swampland restrictions work. The point of the swampland is that an effective field theory looks totally OK as an effective field theory – but there are still some hidden reasons (some potential problems with the completion that you may imagine to reside at the very high, Planckian scales) why it is wrong as a limit of a consistent theory of gravity. Here, they really find out that the effective field theory is self-defeating by itself. While it may be viewed as a "more direct problem" of the effective field theory, I think that it is actually a smaller problem in quantum gravity because there is nothing wrong about the situation when an effective field theory is an incomplete description. Maybe the very high-energy gravitino modes could be incorporated in some way, to get a better approximation of the full quantum gravity.

But if you believe that their principle is correct, it has consequences. You may write the speed as a sum of two ratios; each ratio has something like $$m^4$$ terms in the numerator and the denominator, and all these terms are products of $$m^2$$ (gravitino mass), $$\dot m$$ (the time derivative), $$M_{\rm Pl}^2$$, $$\rho$$, and $$p$$. In some condntions in unlucky enough theories, this may be adjusted to zero. The effective field theory would be killed by the newly proposed principle. Such dead theories would include theories with a very light (collider-scale) gravitino AND the B-mode tensor polarization modes from primordial gravitational waves. So these two things (light gravitino; tensor modes) couldn't exist simultaneously if these folks are right. This conclusion is extracted by efforts to quantize the gravitino at the end of the inflationary epoch.