Perturbative and non-perturbative analysis of defect correlators in AdS/CFT

TL;DR

This thesis advances the understanding of defect correlators in AdS/CFT by combining analytic bootstrap, effective AdS2 theories, and lattice methods to compute and analyze correlators in superconformal defect theories.

Contribution

It introduces new bootstrap calculations, Mellin amplitude formalism for AdS2, and lattice discretization techniques for defect correlators, providing both perturbative and non-perturbative insights.

Findings

Computed four-point correlator in ABJM to third order in strong coupling.

Derived all-order results for the highest logarithm power in the correlator.

Calculated scalar contact Witten diagrams for arbitrary n-point functions.

Abstract

In this thesis, we consider two approaches to the study of correlation functions in one-dimensional defect Conformal Field Theories (dCFT$_1$), in particular those defined by 1/2-BPS Wilson line defects in the three- and four-dimensional superconformal theories relevant in the AdS/CFT correspondence. In the first approach, we use the analytic conformal bootstrap to evaluate two examples of defect correlators. The four-point correlator of the displacement supermultiplet inserted on the 1/2-BPS Wilson line in ABJM theory is computed to the third order in a strong-coupling expansion and reproduces the explicit first-order Witten diagram calculations. The CFT$_1$ data are then extracted from this correlator, and the operator mixing is solved at first order. Consequently, all-order results are derived for the part of the correlator with the highest logarithm power, uniquely determining the double-scaling limit. Then, the five-point correlator of $1/2$-BPS operators inserted on the 1/2-BPS Wilson line in $\mathcal{N}=4$ super Yang-Mills are studied. The superblocks are derived for all channels of the OPE, and the five-point correlator is bootstrapped to first order in a strong coupling expansion. The CFT$_1$ data are then extracted, confirming that operator mixing does not affect the first-order anomalous dimension. The second approach considers the general structure of correlators in effective theories in AdS$_2$. All scalar $n$-point contact Witten diagrams for external operators of integer conformal weight are computed. Effective theories in AdS$_2$ defined by an interaction Lagrangian with an arbitrary number of derivatives are then considered and solved to first order using a new formalism of Mellin amplitudes for 1d CFTs. Finally, the cusped Wilson line discretised action is presented as an alternative way to obtain non-perturbative data: through Lattice Field Theory.