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String sigma-models in AdS/CFT: perturbative and non-perturbative results
(Humboldt U., Berlin)
We study the strong coupling behaviour of 1/4-BPS latitude Wilson loops in N=4 SYM theory, computing the oneloop corrections to the relevant classical string solution in AdS5xS5 in sigma-model perturbation theory. The approach is based on the application of the Gel’fand-Yaglom method to compute the functional determinants for the fluctuations of the type IIB Green-Schwarz action expanded around the minimal-area surface. We normalize the vev of the Wilson loops with respect to the 1/2-BPS circular case to circumvent the problem of determining the overall constant contribution from the normalization of ghost zero modes. We find a discrepancy with the result obtained via localization in the gauge theory, and we discuss some issues that might be responsible for this outcome of the one-loop analysis.
In the second part we discuss a possible discretization of the Green-Schwarz string action in the AdS5xS5 background and its application to the numerical study of the cusp anomalous dimension f(g) of N=4 SYM. This is a pure function of the coupling g and, assuming the integrability of the underlying model, provides an example of non-trivial interpolation smoothly connecting weak and strong coupling regimes and can test the AdS/CFT correspondence.