  Anderson localization is studied for two flavors of massless Dirac fermions
in 2D space perturbed by static disorder that is invariant under a chiral
symmetry (chS) and a time-reversal symmetry (TRS) operation which, when
squared, is equal either to plus or minus the identity. The former TRS
(symmetry class BDI) can for example be realized when the Dirac fermions emerge
from spinless fermions hopping on a 2D lattice with a linear energy dispersion
such as the honeycomb lattice (graphene) or the square lattice with $\pi$-flux
per plaquette. The latter TRS is realized by the surface states of 3D
$\mathbb{Z}_{2}$-topological band insulators in symmetry class CII. In the
phase diagram parametrized by the disorder strengths, there is an infrared
stable line of critical points for both symmetry classes BDI and CII. Here we
discuss a "global phase diagram" in which disordered Dirac fermion systems in
all three chiral symmetry classes, AIII, CII, and BDI, occur in 4 quadrants,
sharing one corner which represents the clean Dirac fermion limit. This phase
diagram also includes symmetry classes AII [e.g., appearing at the surface of a
disordered 3D $\mathbb{Z}_2$-topological band insulator in the spin-orbit
(symplectic) symmetry class] and D (e.g., the random bond Ising model in two
dimensions) as boundaries separating regions of the phase diagram belonging to
the three chS classes AIII, BDI, and CII. Moreover, we argue that physics of
Anderson localization in the CII phase can be presented in terms of a
non-linear-sigma model (NLsM) with a $\mathbb{Z}_{2}$-topological term. We
thereby complete the derivation of topological or Wess-Zumino-Novikov-Witten
terms in the NLsM description of disordered fermionic models in all 10 symmetry
classes relevant to Anderson localization in two spatial dimensions.
