  We discuss quantum electrodynamics emerging in the vacua with anisotropic
scaling. Systems with anisotropic scaling were suggested by Horava in relation
to the quantum theory of gravity. In such vacua the space and time are not
equivalent, and moreover they obey different scaling laws, called the
anisotropic scaling. Such anisotropic scaling takes place for fermions in
bilayer graphene, where if one neglects the trigonal warping effects the
massless Dirac fermions have quadratic dispersion. This results in the
anisotropic quantum electrodynamics, in which electric and magnetic fields obey
different scaling laws. Here we discuss the Heisenberg-Euler action and
Schwinger pair production in such anisotropic QED
