  Spin ice magnetic monopoles are fractionalized emergent excitations in a
class of frustrated magnets called spin ices. The classical spin ice model has
an extensive number of ground state spin configurations, whereas magnetic
monopoles can be thought of as the endpoints of string operators applied to
these ground states. Introducing quantum fluctuations into the model induces
monopoles with dynamics, which would normally lift the degeneracy of the
two-monopole energy level at the linear order of the perturbation. Contrary to
this expectation, we find that quantum fluctuations in the form of a locally
transverse field term partially preserve the extensive degeneracy of the
monopole pairs up to the much weaker splitting of the background monopole-free
spin ice configurations. Each of these approximately degenerate excited states,
termed mesons, can be represented as a bound monopole-antimonopole pair
delocalized in a classical spin ice background.
