LAUSR

A bstractWe 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 Sa×ℍb$$ {\mathbb{S}}^a \times {\mathrm{\mathbb{H}}}^b $$, which are conformally related to Sa+b$$ {{\mathbb{S}}^a}^{+b} $$. For the case of a = 1, related to the entanglement entropy across Sb−1$$ {{\mathbb{S}}^b}^{-1} $$, we provide some new explicit computations of entanglement entropies at weak coupling. We then compute the free energy for spaces Sa×ℍb$$ {\mathbb{S}}^a \times {\mathrm{\mathbb{H}}}^b $$ for different values of a and b. For spaces S2n+1×ℍ2k$$ {\mathbb{S}}^{2n+1}\times {\mathrm{\mathbb{H}}}^{2k} $$ we find an exact match with the free energy on S2n+2k+1$$ {\mathbb{S}}^{2n+2k+1} $$. For ℍ2k + 1 and S3×ℍ3$$ {\mathbb{S}}^3 \times {\mathrm{\mathbb{H}}}^3 $$ we find conformal anomalies originating from boundary terms. We also compute the free energy for strongly coupled theories through holography, obtaining similar results.