D1-brane correction to a line operator index

TL;DR

This paper computes the finite $k$ correction to the line operator index in ${ m AdS}_5$ for ${ m f N}=4$ $U(N)$ SYM, by analyzing D1-brane fluctuations, addressing a mismatch with gauge theory predictions.

Contribution

It introduces a method to calculate finite $k$ corrections via D1-brane fluctuations, providing new insights into line operator indices in AdS/CFT correspondence.

Findings

Calculated leading finite $k$ correction to the line operator index.

Analyzed D1-brane fluctuation modes in the AdS background.

Addressed the mismatch between gauge theory and gravity side predictions.

Abstract

Wilson line operators in the rank $k$ totally symmetric tensor representation of ${\cal N}=4$ $U(N)$ 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.