# On the entanglement contour of excited states in the holographic CFT

## TL;DR

This paper explores the structure of entanglement in excited states of holographic 2d CFTs, linking it to thermodynamics and the first law of entanglement, with explicit examples and discussions on complexity.

## Contribution

It derives the entanglement contour for time-dependent excited states in holographic 2d CFTs using the partial entanglement entropy proposal, connecting it to thermodynamics.

## Key findings

- Entanglement contour relates to the first law of entanglement.
- Explicit derivation for time-dependent excited states.
- Discussion on coarse-graining and complexity in AdS3/CFT2.

## Abstract

In this paper, we study the entanglement contour in a general excited state in the holographic 2d CFT using the partial entanglement entropy proposal. We show how thermodynamics fixes the entanglement contour relating it to the first law of entanglement. We derive the entanglement contour for a general time-dependent excited state and consider a quenched initial state in the presence of spatial boundaries as an explicit example. Finally, we comment on the coarse-graining and the complexity contour in the $AdS_3/CFT_2$.