  We discuss a non-fermi liquid gapless metallic surface state of the
topological band insulator. It has an odd number of gapless Dirac fermions
coupled to a non-compact U(1) gauge field. This can be viewed as a vortex dual
to the conventional Dirac fermion surface state. This surface duality is a
reflection of a bulk dual description discussed recently for the gauged
topological insulator. All the other known surface states can be conveniently
accessed from the dual Dirac liquid, including the surface quantum hall state,
the Fu-Kane superconductor, the gapped symmetric topological order and the
"composite Dirac liquid". We also discuss the physical properties of the dual
Dirac liquid, and its connection to the half-filled Landau level.
