On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM

Details On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM

2007-07-06

arxiv.org/abs/0707.1031v3

JHEP 0710:031,2007

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, v2: references added, sign inconsistency resolved in (5.5,5.6), v3: Section 3.4 on Hamiltonian added, minor improvem

Scientific paper

10.1088/1126-6708/2007/10/031

Strong evidence indicates that the spectrum of planar anomalous dimensions of N=4 super Yang-Mills theory is given asymptotically by Bethe equations. A curious observation is that the Bethe equations for the psu(1,1|2) subsector lead to very large degeneracies of 2^M multiplets, which apparently do not follow from conventional integrable structures. In this article, we explain such degeneracies by constructing suitable conserved nonlocal generators acting on the spin chain. We propose that they generate a subalgebra of the loop algebra for the su(2) automorphism of psu(1,1|2). Then the degenerate multiplets of size 2^M transform in irreducible tensor products of M two-dimensional evaluation representations of the loop algebra.

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