  We present a microscopic quantum theory of light-matter interaction in
pristine sheets of two-dimensional semiconductors coupled to localized
electromagnetic resonators such as optical nanocavities or plasmonic particles.
The light-matter interaction breaks the translation symmetry of excitons in the
two-dimensional lattice, and we find that this symmetry-breaking interaction
leads to the formation of a localized exciton state, which mimics the spatial
distribution of the electromagnetic field of the resonator. The localized
exciton state is in turn coupled to an environment of residual exciton states.
We quantify the influence of the environment and find that it is most
pronounced for small lateral confinement length scales of the electromagnetic
field in the resonator, and that environmental effects can be neglected if this
length scale is sufficiently large. The microscopic theory provides a
physically appealing derivation of the coupled oscillator models widely used to
model experiments on these types of systems, in which all observable quantities
are directly derived from the material parameters and the properties of the
resonant electromagnetic field. As a consistency check, we show that the theory
recovers the results of semiclassical electromagnetic calculations and
experimental measurements of the excitonic dielectric response in the linear
excitation limit. The theory, however, is not limited to linear response, and
in general describes nonlinear exciton-exciton interactions in the localized
exciton state, thereby providing a powerful means of investigating the
nonlinear optical response of such systems.
