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We discuss conformal field theories (CFTs) in rectangular geometries, anddevelop a formalism that involves a conformal boundary state for the 1+1d opensystem. We focus on the case of homogeneous boundary conditions (no insertionof a boundary condition changing operator), for which we derive an explicitexpression of the associated boundary state, valid for any arbitrary CFT. Wecheck the validity of our solution, comparing it with known results forpartition functions, numerical simulations of lattice discretizations, andcoherent state expressions for free theories.

Conformal boundary state for the rectangular geometry