# Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT$_1$

Bianchi, L., Bliard, G., , Griguolo, L. and Seminara, D. (2020). Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT$_1$. Journal of High Energy Physics, 2020(8), 143..

## Abstract

We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT$_1$ with SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS$_4 \times \mathbb{C}\textrm{P}^3$ ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-point correlators of its components in terms of a single function of the one-dimensional cross-ratio. Such function is highly constrained by crossing and internal consistency, allowing us to use an analytical bootstrap approach to find the first subleading correction at strong coupling. Finally, we use AdS/CFT to compute the same four-point functions through tree-level AdS$_2$ Witten diagrams, producing a result that is perfectly consistent with the bootstrap solution.

Publication Type: Article © The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Q Science > QA Mathematics School of Mathematics, Computer Science & Engineering > Mathematics 18 Sep 2020 15:16 https://openaccess.city.ac.uk/id/eprint/24882
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