On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian

TL;DR

This paper constructs Drinfeld's second realization of the Yangian symmetry for the AdS/CFT su(2|2) algebra, clarifying its structure, isomorphism with the first realization, and implications for finite-dimensional representations.

Contribution

It provides the explicit construction and proof of isomorphism of Drinfeld's second realization for the AdS/CFT su(2|2) Yangian, including corrections for central charges.

Findings

Second realization is isomorphic to the first, with necessary corrections for central charges.

The second realization facilitates studying finite-dimensional representations.

Rapidity variables are boosted by energy eigenvalues in the fundamental representation.

Abstract

We construct Drinfeld's second realization of the Yangian based on psu(2|2)xR^3 symmetry. The second realization is traditionally more suitable for deriving the quantum double and the universal R matrix with respect to the first realization, originally obtained by Beisert, and it is generically more useful in order to study finite dimensional representations. We show that the two realization are isomorphic, where the isomorphism is almost the standard one given by Drinfeld for simple Lie algebras, but needs some crucial corrections to account for the central charges. We also evaluate the generators of the second realization on the fundamental representation, finding the interesting result that the rapidity variable for some generators gets boosted by the energy eigenvalue.