Abstract
We obtain the ratio of semiclassical partition functions for the extension under mixed flux of the minimal surfaces subtending a circumference and a line in Euclidean $AdS_{3}\times S^{3}\times T^{4}$. We reduce the problem to the computation of a set of functional determinants. If the Ramond-Ramond flux does not vanish, we find that the contribution of the $B$-field is comprised in the conformal anomaly. In this case, we successively apply the Gel'fand-Yaglom method and the Abel-Plana formula to the flat-measure determinants. To cancel the resultant infrared divergences, we shift the regularization of the sum over half-integers depending on whether it corresponds to massive or massless fermionic modes. We show that the result is compatible with the zeta-function regularization approach. In the limit of pure Neveu-Schwarz-Neveu-Schwarz flux we argue that the computation trivializes. We extend the reasoning to other surfaces with the same behavior in this regime.
Highlights
The connection between Wilson loops and minimal surfaces raised a milestone in the AdS=CFT correspondence
The original proposal establishes that the strong coupling limit of the expectation value of a Wilson loop in N 1⁄4 4 supersymmetric Yang-Mills in four dimensions is given by the regularized minimal area swept by a string probe propagating in Euclidean AdS5 × S5 and terminating in the contour of the Wilson loop on the boundary of the Euclidean anti-de Sitter space [1,2]
In this article we have studied the difference between one-loop effective actions of the extension under mixed R-R and NS-NS three-form fluxes of the minimal surfaces subtending a circle and a line at the boundary of Euclidean anti-de Sitter space
Summary
The connection between Wilson loops and minimal surfaces raised a milestone in the AdS=CFT correspondence. In this article we will analyze the one-loop effective action of the extension under fluxes of the minimal area surface subtending a circumference This solution constitutes an appropriate framework for the study of the mixed flux regime in the semiclassical picture, since it is simple enough to allow a tractable analysis but still comprises the major features that are meant to be brought in. We will follow the analysis of [6] and introduce the deformation under mixed fluxes of the classical worldsheet subtending a line as a reference solution, as it shares the same behavior with this surface in the vicinity of the boundary In this way, we will be able to consider the ratio of both semiclassical partition functions, for which infrared divergences are expected to cancel. We have relegated the details on the application of the Gel’fand-Yaglom method and the Abel-Plana formula to the appendixes
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