D1-brane correction to a line operator index

A bstract Wilson line operators in the rank k totally symmetric tensor representation of $$\mathcal{N}=4 \text{U}(N)$$ sypersymmetric Yang-Mills theories are expected to be realized as D3-branes expanded in AdS 5 . Although there is a mismatch between the corresponding line operator indices even in the large N and large k limit, it is possible to calculate the finite k correction on the AdS side as the contribution from D1-branes. We analyze D1-brane fluctuation modes and calculate the leading finite k correction to the line operator index on the AdS side.