  We extend coupled-cluster theory performed on top of a Slater determinant
breaking rotational symmetry to allow for the exact restoration of the angular
momentum at any truncation order. The main objective relates to the description
of near-degenerate finite quantum systems with an open-shell character. As
such, the newly developed many-body formalism offers a wealth of potential
applications and further extensions dedicated to the ab initio description of,
e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism,
which encompasses both single-reference coupled cluster theory and projected
Hartree-Fock theory as particular cases, permits the computation of usual sets
of connected diagrams while consistently incorporating static correlations
through the highly non-perturbative restoration of rotational symmetry.
Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy
associated with each angular momentum, is accessed within a single calculation.
A key difficulty presently overcome relates to the necessity to handle
generalized energy {\it and} norm kernels for which naturally terminating
coupled-cluster expansions could be eventually obtained. The present work
focuses on $SU(2)$ but can be extended to any (locally) compact Lie group and
to discrete groups, such as most point groups. In particular, the formalism
will be soon generalized to $U(1)$ symmetry associated with particle number
conservation. This is relevant to Bogoliubov coupled cluster theory that was
recently formulated and applied to singly open-shell nuclei.
