• A new paper by Luis Alvarez-Gaume, Orestis Loukas, Domenico Orlando, and Susanne Reffert called Compensating strong coupling with large charge appeared today. In one sentence, they prove that if you consider a QFT with global symmetries and focus on the sector of the Hilbert space where states have large global charge, then
    1. There are Goldstone excitations in $\mathcal{L}_{\mathrm{eff}}$
    2. The effective couplings are suppressed by powers of the global charge (and therefore are small if the global charge is large).

    The QFT considered here are not necessarily relativistic (a relativistic theory has to be treated as a non-relativistic one if the vacuum breaks time translation symmetry), and a generalization of the well-known Goldstone theorem is needed.

  • In a series of talks in 2005, Vafa introduced the concept of Swampland, which is the region around the string theory landscape made of consistent-looking semiclassical effective field theories, which are actually inconsistent. It is important to find criteria that can exclude a theory from the consistent landscape and push it back into the swampland. One such criterion is the following:

    Gravity is the weakest force.

    This is called the Weak Gravity Conjecture (WGC), and it states more precisely that there exist a particle such that $m \leq |Q|$, where $Q$ is the charge in suitable units. Recently, Ooguri and Vafa applied the same idea to branes, and conjecture that

    The inequality is saturated   iff   States are BPS

    This seemingly innocuous generalization of WGC implies that non-supersymmetric AdS vacua supported by fluxes must be unstable and that their effective theories belong to the swampland, even if theymay look consistent!
    In the same vein, the Vacua Morghulis incantation goes even further and asserts that non-supersymmetric vacua in string theory are at most metastable and eventually decay, while supersymmetric vacua are only marginally stable. Note however that some people think otherwise.

  • La médaille d'or du CNRS a été décernée récemment à Claire Voisin pour ses travaux en géométrie algébrique. J'y reviendrai prochainement, mais je signale déjà les bons articles de vulgarisation parus sur Images des Mathématiques, ici et là.