  Parity-Time ($\mathcal{PT}$) symmetry has become an important concept in the
design of synthetic optical materials, with exotic functionalities such as
unidirectional transport and non-reciprocal reflection. At exceptional points,
this symmetry is spontaneously broken, and solutions transition from those with
conserved intensity to exponential growth or decay. Here we analyze a
quantum-photonic surface formed by a single layer of atoms in an array with
light mediating strong cooperative many-body interactions. We show how
delocalized collective excitation eigenmodes can exhibit an effective
$\mathcal{PT}$ symmetry and non-exponential decay. This effective symmetry is
achieved in a passive system without gain by balancing the scattering of a
bright mode with the loss from a subradiant dark mode. These modes coalesce at
exceptional points, evidenced by the emergence of coherent perfect absorption
where coherent incoming light is perfectly absorbed and scattered only
incoherently. We also show how $\mathcal{PT}$ symmetry can be generated in
total reflection and by balancing scattering and loss between different
polarizations of collective modes.
