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

Spill, F and Torrielli, A (2009) On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian JOURNAL OF GEOMETRY AND PHYSICS, 59 (4). 489 - 502. ISSN 0393-0440

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Abstract

We construct Drinfeld’s second realization of the Yangian based on psu(2|2) ⋉ R3 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 realizations 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.

Item Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Geometry and Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Geometry and Physics, 59(4), April 2009, DOI 10.1016/j.geomphys.2009.01.001.
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Physics, Mathematical, Mathematics, Physics, Yangians, AdS/CFT correspondence, Integrable systems, ADS(5) X S-5, SIMPLE LIE-SUPERALGEBRAS, UNIVERSAL R-MATRICES, GIANT MAGNONS, N=4 SYM, DILATATION OPERATOR, BETHE-ANSATZ, MILLS THEORY, SPIN CHAIN, STRINGS
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 13 Jan 2012 10:49
Last Modified: 23 Sep 2013 18:57
URI: http://epubs.surrey.ac.uk/id/eprint/72389

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