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

TL;DR

This paper investigates the large degeneracies in the psu(1,1|2) sector of N=4 SYM's spectrum, explaining them through the construction of conserved nonlocal generators related to the loop algebra.

Contribution

It introduces a novel explanation for degeneracies in the psu(1,1|2) sector by constructing nonlocal conserved generators linked to the loop algebra.

Findings

Degeneracies correspond to tensor products of evaluation representations.

Conserved nonlocal generators form a subalgebra of the loop algebra.

Degenerate multiplets are explained via irreducible tensor products.

Abstract

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.