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October 12, 2025Open Access

Continuous spin field in the AdS₆ space

Key Points

Casimir operators were explicitly derived for the so(2,5) algebra, revealing their relationship with continuous spin fields.
The framework incorporates the Lie-Lorentz derivative, crucial for understanding the geometry of AdS6 and its spin dynamics.
Operator constraints derived for continuous spin fields generalize known constraints in six-dimensional Minkowski space.
Eigenvalues of Casimir operators determined by a dimensional parameter and a half-integer s highlight the uniqueness of these representations.

Abstract

A representation of the so (2, 5) algebra corresponding to the continuous spin field in AdS₆ is considered. The algebra is realized using the Lie-Lorentz derivative, which naturally incorporates AdS₆ geometry and spin degrees of freedom. Within this framework, we derive explicit expressions for the Casimir operators in terms of both the covariant derivative and the spin invariants. The continuous spin representation under consideration is defined by a system of operator constraints that generalize those known for six-dimensional Minkowski space. We demonstrate that these constraints completely fix all Casimir operators of the so (2, 5) algebra, with the eigenvalues determined by a dimensional real parameter μ and a positive (half-) integer s.

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