Precision matching of circular Wilson loops and strings in AdS₅xS⁵

Authors: Daniel Medina-Rincon, Arkady A. Tseytlin and Konstantin Zarembo

Preprint number: UUITP-15/18

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 AdS₅xS⁵ 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, following arXiv:1712.07730, 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.