Super-light baryphotons, Weak Gravity Conjecture and Exotic instantons in Neutron-Antineutron transitions

In companion papers \cite{Addazi:2015pia,Addazi:2016rgo}, we have discussed current bounds of a new super-light baryo-photon, associated to a $U(1)_{B-L}$ gauged, from neutron-antineutron current data, which are competitive with E\"otv\"os type experiments. Here, we discuss the implications of a possible baryo-photon detection in string theory and quantum gravity. The discovery of a very light gauge boson should imply the violation of the Weak Gravity Conjecture, carrying deep consequences in our understanding of holography, quantum gravity and black holes. On the other hand, we show how the detection of a baryo-photon would also exclude the generation of all $B{-}L$ violating operators from Exotic Stringy Instantons. We will disclaim the common statement in literature that neutron-antineutron may indirectly test at least a $300-1000\, \rm TeV$ scale. Searches of baryo-photons can provide indirect informations of the Planck (or String) scale (quantum black holes, holography and non-perturbative stringy effects). This strongly motivates new neutron-antineutron experiments with adjustable magnetic fields dedicated to the detection of super-light baryo-photons.