Non-conformal Line Defect (Shell Operator) in AdS$_3$/CFT$_2$: Spinning and Higher Point Correlators

TL;DR

This paper extends the understanding of non-conformal line defects in AdS$_3$/CFT$_2$ by computing spinning defect correlators and higher point functions, revealing their complex behavior and matching with gravitational and ETH analyses.

Contribution

It introduces the computation of spinning defect correlators and higher point functions, showing their dependence on defect order and deviations from standard junction conditions.

Findings

Spinning defect correlators differ from scalar defect correlators.

Higher point correlators depend on defect insertion order.

Matching between field theory, ETH, and gravity is confirmed.

Abstract

Recently, a special type of non-conformal line defect, known as thin-shell operator, has played a key role in demonstrating the chaotic nature of the high energy sector in AdS$_3$/CFT$_2$. The chaotic nature was revealed concretely through a matching among the vacuum Virasoro block in holographic CFT$_2$, ETH analysis, and gravitational on-shell partition function in AdS$_3$ with nontrivial backreaction. In this work, we generalize this matching in two ways. First, we compute two-point correlator of the spinning defects, in contrast to previous scalar defect correlator, in both the microcanonical ensemble and the canonical ensemble. Holographically, these spinning defects correspond to bulk domain walls composed of dust particles with angular momentum. Using the first order formalism of gravity, it is shown that the junction condition deviates from Israel's junction condition, resulting in a discontinuous metric across the domain wall. Second, we calculate general higher point correlators involving multiple scalar defects and provide a detailed example with four defects. We see explicitly that, because line operators in CFT$_2$ are codimension one objects, the correlators depend on the order in which these nonlocal defects are inserted, unlike the Euclidean correlators of local operators. In both generalizations, we achieve a precise matching between field theory solutions, ETH analysis and gravitational on-shell actions.