One-loop corrections to a holographic Wilson loop in AdS4 × ℂℙ3

The evaluation of BPS (Bogomol’nyi-Prasad-Sommerfeld) Wilson loops in N = 6, D = 3 Chern-Simons matter theory is reduced to ordinary matrix integrals via a localization technique. That the vacuum expectation value of 1/2 BPS Wilson loops at leading order in the planar limit agrees with the regularized classical string action is easy to check via AdS/CFT. Then, the subleading terms, in principle, can be calculated by treating the string theory semiclassically. In this article, we calculate the one-loop determinant for the fluctuation modes of a holographic Wilson loop as a IIA string in the dual geometry AdS4 × ℂℙ3. The fermionic normal mode frequencies are expressed in terms of the hypergeometric function, and the one-loop effective action is computed numerically. The discrepancy compared to the localization formula is due to the zero mode normalization constant, which has yet to be determined.