Super Yangian of superstring on $\mathrm{AdS}_5 × S^5$ revisited

Abstract

We construct infinite number of conserved nonlocal charges for type IIB superstring on the $\mathrm{AdS}_5×S^5$ space in the conformal gauge without assuming any $\kappa$ gauge fixing, and show that they satisfy the super Yangian algebra. The resultant algebra is the same as our previous work, where a special gauge was assumed in such a way that the Noether current satisfies a flatness condition. However the flatness condition for the Noether current of a superstring on the AdS space is broken in general. We show that the anomalous contribution is absorbed into the current where fermionic constraints play an essential role, and a resultant conserved nonlocal charge has different expression satisfying the same super Yangian algebra.