Free energy and boundary anomalies on S(a)xH(b) spaces

We compute free energies as well as conformal anomalies associated with boundaries for a conformal free scalar field. To that matter, we introduce the family of spaces of the form S(a)xH(b), which are conformally related to S(a+b). For the case of a=1, related to the entanglement entropy across S(b-1), we provide some new explicit computations of entanglement entropies at weak coupling. We then compute the free energy for spaces S(a)xH(b) for different values of a and b. For spaces S(2n+k)xH(2k) we find an exact match with the free energy on S(2n+2k+1). For H(2k+1) and S(3)xH(3) we find conformal anomalies originating from boundary terms. We also compute the free energy for strongly coupled theories through holography, obtaining similar results.