Scalar field on AdS: quantum one loop "in one line"

It is shown that quantum one-loop potentials of the bulk fields in the Randall and Sundrum (RS) model may be immediately expressed in integrals with use of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants. Simple expression is obtained for the UV-finite difference of one-loop quantum energies for two arbitrary values of parameter of the double-trace asymptotic boundary condition in one-brane and two-brane RS-models. Compact formula for Schwinger-DeWitt expansion gives values of induced Planck mass and induced gauge coupling constant in transverse space. S-DW expansion is plagued by IR-divergences in one-brane RS-model and makes sense in two-brane model.

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