# Light-cone continuous-spin field in AdS space

## TL;DR

This paper develops a light-cone gauge approach for continuous-spin fields in AdS space, deriving the Lagrangian, symmetry realizations, and exploring potential AdS/CFT dualities, including reducible models involving various spins.

## Contribution

It introduces a light-cone gauge formulation for continuous-spin fields in AdS space and explores their symmetry properties and dualities, extending previous theoretical frameworks.

## Key findings

- Derived light-cone gauge Lagrangian for continuous-spin fields.
- Realized relativistic symmetry operators explicitly.
- Identified reducible models involving multiple spins.

## Abstract

We develop further the general light-cone gauge approach in AdS space and apply it for studying continuous-spin field. For such field, we find light-cone gauge Lagrangian and realization of relativistic symmetries. We find a simple realization of spin operators entering our approach. Generalization of our results to the gauge invariant Lagrangian formulation is also described. We conjecture that, in the framework of AdS/CFT, the continuous-spin AdS field is dual to light-ray conformal operator. For some particular cases, our continuous-spin field leads to reducible models. We note two reducible models. The first model consists of massive scalar, massless vector, and partial continuous-spin field involving fields of all spins greater than one, while the second model consists of massive vector, massless spin-2 field, and partial continuous-spin field involving all fields of spins greater than two.