We compute the one-loop correction to the probe D3-brane action in $Ad{S}_5\times S^5$ expanded around the classical Drukker–Fiol solution ending on a circle at the boundary. It is essentially the logarithm of the one-loop partition function of an Abelian $\mathcal{N}=4$ vector multiplet in $Ad{S}_2\times S^2$ geometry. This one-loop correction should be describing the subleading $1/N$ term in the expectation value of circular Wilson loop in the totally symmetric rank $k$ representation in $SU(N)$ supersymmetric Yang-Mills theory at strong coupling. In the limit $1\ll k\ll N$ when the circular Wilson loop expectation values for the symmetric representation and for the product of $k$ fundamental representations are expected to match, we find that this one-loop D3-brane correction agrees with the gauge theory result for the $k$-fundamental case.

• Received 29 April 2014

DOI:https://doi.org/10.1103/PhysRevD.89.126008