  We discuss conformal field theories (CFTs) in rectangular geometries, and
develop a formalism that involves a conformal boundary state for the 1+1d open
system. We focus on the case of homogeneous boundary conditions (no insertion
of a boundary condition changing operator), for which we derive an explicit
expression of the associated boundary state, valid for any arbitrary CFT. We
check the validity of our solution, comparing it with known results for
partition functions, numerical simulations of lattice discretizations, and
coherent state expressions for free theories.
