Currents of Arbitrary Spin in $AdS_3$

TL;DR

This paper investigates conserved currents of arbitrary spin in $AdS_3$, revealing their unique properties and potential holographic implications, especially regarding their exactness and higher-derivative structures.

Contribution

It demonstrates that 2-forms dual to conserved currents in $AdS_3$ are exact within infinite higher-derivative expansions, a feature absent in flat space.

Findings

2-forms dual to currents are exact in $AdS_3$

Exactness involves inverse powers of the cosmological constant

No flat space analog for this property

Abstract

We study conserved currents of any integer or half integer spin built from massless scalar and spinor fields in $AdS_3$. 2-forms dual to the conserved currents in $AdS_3$ are shown to be exact in the class of infinite expansions in higher derivatives of the matter fields with the coefficients containing inverse powers of the cosmological constant. This property has no analog in the flat space and may be related to the holography of the AdS spaces.