Abstract
We examine the one-loop partition function describing the fluctuations of the superstring in a Schwarzschild-${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ background. On the bosonic side, we demonstrate the one-loop equivalence of the Nambu-Goto action and the Polyakov action for a general world sheet, while on the fermionic side, we consider the reduction of the ten-dimensional Green-Schwarz fermion action to a two-dimensional world sheet action. We derive the partition functions of the world sheets corresponding to both straight and parallel Wilson lines. We discuss the cancellation of the UV divergences of the functional determinants in the thermal AdS background.
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