  Topological semimetals are gapless states of matter which have robust and
unique electromagnetic responses and surface states. In this paper, we consider
semimetals which have point like Fermi surfaces in various spatial dimensions
$D=1,2,3$ which naturally occur in the transition between a weak topological
insulator and a trivial insulating phase. These semimetals include those of
Dirac and Weyl type. We construct these phases by layering strong topological
insulator phases in one dimension lower. This perspective helps us understand
their effective response field theory that is generally characterized by a
1-form $b$ which represents a source of Lorentz violation and can be read off
from the location of the nodes in momentum space and the helicities/chiralities
of the nodes. We derive effective response actions for the 2D and 3D Dirac
semi-metals, and extensively discuss the response of the Weyl semimetal. We
also show how our work can be used to describe semi-metals with Fermi-surfaces
with lower co-dimension as well as to describe the topological response of 3D
topological crystalline insulators.
