We study string quantum corrections to the ratio of latitude and circular Wilson loops in N = 4 super-Yang-Mills theory at strong coupling. Conformal gauge for the corresponding minimal surface in AdS 5 × S 5 is singular and we show that an IR anomaly associated with the divergence in the conformal factor removes previously reported discrepancy with the exact field-theory result. We also carefully check conformal anomaly cancellation and recalculate fluctuation determinants by directly evaluating phaseshifts for all the fluctuation modes.
We show that bosonic spinning strings on the η-deformed AdS 5 ×S 5 background are naturally described as periodic solutions of a novel finite-dimensional integrable system which can be viewed as a deformation of the celebrated Neumann model. For this deformed model we find the Lax representation and the analogue of the Uhlenbeck integrals.
Previous attempts to match the exact N = 4 super Yang-Mills expression for the expectation value of the 1 2 -BPS circular Wilson loop with the semiclassical AdS 5 × S 5 string theory prediction were not successful at the first subleading order. There was a missing prefactor ∼ λ −3 4 which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing the ratio of the string partition functions corresponding to the circular Wilson loop and the special 1 4 -supersymmetric latitude Wilson loop. The fact that the latter has a trivial expectation value in the gauge theory allows us to relate the prefactor to the contribution of the three zero modes of the "transverse" fluctuation operator in the 5-sphere directions.
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