  We discuss some aspects of critical electric and magnetic fields in a field
theory with holographic dual description. We extend the analysis of
arxiv:1109.2920, which finds a critical electric field at which the Schwinger
pair production barrier drops to zero, to the case of magnetic fields. We first
find that, unlike ordinary weakly coupled theories, the magnetic field is not
subject to any perturbative instability originating from the presence of a
tachyonic ground state in the W-boson spectrum. This follows from the large
value of the 't Hooft coupling \lambda, which prevents the Zeeman interaction
term to overcome the particle mass at high B. Consequently, we study the next
possible B-field instability, i.e. monopole pair production, which is the
S-dual version of the Schwinger effect. Also in this case a critical magnetic
field is expected when the tunneling barrier drops to zero. These
Schwinger-type criticalities are the holographic duals, in the bulk, to the
fields E or B reaching the tension of F1 or D1 strings respectively. We then
discuss how this effect is modified when electric and magnetic fields are
present simultaneously and dyonic states in the spectrum can be pair produced
by a generic E - B background. Finally, we analyze finite temperature effects
on Schwinger criticalities, i.e. in the AdS-Schwarzshild black hole background.
