# On some (integrable) structures in low-dimensional holography

## TL;DR

This paper explores the role of integrable structures and invariants in low-dimensional holography, focusing on entanglement entropy, projective invariants, and their potential in higher spin theories.

## Contribution

It revisits the role of invariants in low-dimensional holography and proposes generalizations to higher spin theories, highlighting the significance of quadratic invariant deformations.

## Key findings

- Entanglement entropy relates to projective invariants in 2d CFT.
- Higher projective invariants are considered for higher spin holography.
- Quadratic invariant deformations may influence low-dimensional higher spin holography.

## Abstract

Recent progress in holographic correspondence uncovered remarkable relations between key characteristics of the theories on both sides of duality and certain integrable models. In this note we revisit the problem of the role of certain invariants in low-dimensional holography. As motivating example we consider first the entanglement entropy in 2d CFT and projective invariants. Next we consider higher projective invariants and suggest generalization to higher spin theories. Quadratic in invariants deformations is considered and conjectured to play role in low-dimensional higher spin holography.