Abstract
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 \( {\mathbb{S}}^a \times {\mathrm{\mathbb{H}}}^b \), which are conformally related to \( {{\mathbb{S}}^a}^{+b} \). For the case of a = 1, related to the entanglement entropy across \( {{\mathbb{S}}^b}^{-1} \), we provide some new explicit computations of entanglement entropies at weak coupling. We then compute the free energy for spaces \( {\mathbb{S}}^a \times {\mathrm{\mathbb{H}}}^b \) for different values of a and b. For spaces \( {\mathbb{S}}^{2n+1}\times {\mathrm{\mathbb{H}}}^{2k} \) we find an exact match with the free energy on \( {\mathbb{S}}^{2n+2k+1} \). For ℍ2k + 1 and \( {\mathbb{S}}^3 \times {\mathrm{\mathbb{H}}}^3 \) we find conformal anomalies originating from boundary terms. We also compute the free energy for strongly coupled theories through holography, obtaining similar results.
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Rodriguez-Gomez, D., Russo, J.G. Free energy and boundary anomalies on \( {\mathbb{S}}^a \times {\mathrm{\mathbb{H}}}^b \) spaces. J. High Energ. Phys. 2017, 84 (2017). https://doi.org/10.1007/JHEP10(2017)084
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DOI: https://doi.org/10.1007/JHEP10(2017)084