On symmetry enhancement in the 𝔭𝔰𝔲(1, 1|2) sector of 𝒩 = 4 SYM

Abstract

Strong evidence indicates that the spectrum of planar anomalous dimensions of = 4 super Yang-Mills theory is given asymptotically by Bethe equations. A curious observation is that the Bethe equations for the (1, 1|2) subsector lead to very large degeneracies of 2M 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 (2) automorphism of (1, 1|2). Then the degenerate multiplets of size 2M transform in irreducible tensor products of M two-dimensional evaluation representations of the loop algebra.