Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-02-19
JHEP 0909:097,2009
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, 1 figure, v2: on exceptional superalgebra, previous incorrect comments removed and new sections added, v3: clarifica
Scientific paper
10.1088/1126-6708/2009/09/097
It was shown that the spin chain model coming from AdS/CFT correspondence satisfies the Yangian symmetry if we assume evaluation representation, though so far there is no explicit proof that the evaluation representation satisfies the Serre relation, which is one of the defining equations of the Yangian algebra imposing constraints on the whole algebraic structure. We prove completely that the evaluation representation adopted in the model satisfies the Serre relation by introducing a three-dimensional gamma matrix. After studying the Serre relation, we proceed to the whole Yangian algebraic structure, where we find that the conventional construction of higher grade generators is singular and we propose an alternative construction. In the discussion of the higher grade generators, a great simplification for the proof of the Serre relation is found. Using this expression, we further show that the proof is lifted to the exceptional superalgebra, which is a non-degenerate deformation of the original superalgebra.
Matsumoto Takuya
Moriyama Sanefumi
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