The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling

Understand

We compute the one-loop correction to the probe D3-brane action in AdS5 x S5 expanded around the classical Drukker-Fiol solution ending on a circle at the boundary.

• It is given essentially by the logarithm of the one-loop partition function of an Abelian ${\cal N}=4$ vector multiplet in AdS2 x S2 geometry.
• This one-loop correction is expected to describe the subleading 1/N term in the expectation value of circular Wilson loop in the totally symmetric rank k representation in SU(N) SYM theory at strong coupling.
• In the limit k << 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.