  Compact nonlocal Abelian gauge theory in (2+1) dimensions, also known as loop
model, is a massless theory with a critical line that is explicitly covariant
under duality transformations. It corresponds to the large N_F limit of
self-dual electrodynamics in mixed three-four dimensions. It also provides a
bosonic description for surface excitations of three-dimensional topological
insulators. Upon mapping the model to a local gauge theory in (3+1) dimensions,
we compute the spectrum of electric and magnetic solitonic excitations and the
partition function on the three torus T_3. Analogous results for the S^2 x S^1
geometry show that the theory is conformal invariant and determine the
manifestly self-dual spectrum of conformal fields, corresponding to
order-disorder excitations with fractional statistics.
