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Then

E. I. Buchbinder and A. A. Tseytlin, 1/N correction in the D3-brane description of a circular Wilson loop at strong coupling
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2014
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M. S. Bianchi, L. Griguolo, M. Leoni, S. Penati, and D. Seminara, BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
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2014
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2016
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A. Faraggi, L. A. Pando Zayas, G. A. Silva, and D. Trancanelli, Toward precision holography with supersymmetric Wilson loops
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2016
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2018

Toward Precision Holography in Type IIA with Wilson Loops

Aguilera-Damia, Jeremías, Faraggi, Alberto, Zayas, Leopoldo A. Pando et al.

Understand

We study the one-loop effective action of certain classical type IIA string configurations in $AdS_4\times \mathbb{CP}^3$.

These configurations are dual to Wilson loops in the $\mathcal{N}= 6\:$ $U(N)_k \times U(N)_{-k}$ Chern-Simons theory coupled to matter whose expectation values are known via supersymmetric localization.
We compute the one-loop effective actions using two methods: perturbative heat kernel techniques and full $\zeta$-function regularization.
We find that the result of the perturbative heat kernel method matches the field theory prediction at the appropriate order while the $\zeta$-function approach seems to lead to a disagreement.