Abstract
We construct a long-range Baxter equation encoding anomalous dimensions of composite operators in the SL(2|1) sector of N=4 supersymmetric Yang–Mills theory. The formalism is based on the analytical Bethe ansatz. We compare predictions of the Baxter equations for short operators with available multiloop perturbative calculations.
Highlights
With the discovery of integrable structures1 in QCD [3, 4, 5] and maximally supersymmetric Yang-Mills theory [6, 7, 8, 9] it appears that understanding of strong coupling behavior of anomalous dimensions of composite operators is within reach, at least in the latter gauge theory
The dilatation operators in the large−Nc limit is identified with a known Hamiltonian of a noncompact Heisenberg magnet with the quantum space in all sites corresponding to infinite-dimensional representations ofconformal symmetry algebra of gauge theory Lagrangians
The Bethe Ansatz approach to multiloop dilatation operator in N = 4 super-Yang-Mills theory was successfully undertaken in Ref. [12, 13] culminating with conjectured long-range Bethe Ansatz equations for the P SU(2, 2|4) spin chain [14]
Summary
With the discovery of integrable structures in QCD [3, 4, 5] and maximally supersymmetric Yang-Mills theory [6, 7, 8, 9] it appears that understanding of strong coupling behavior of anomalous dimensions of composite operators is within reach, at least in the latter gauge theory. There are two generic approaches to integrable models, one based on (nested) Bethe Ansatz [10] and another relying on the Baxter equation [11] While both give identical results for models based on representations with highest and/or lowest weight vectors, the Baxter framework applies even when the pseudovacuum state in the Hilbert space of the chain is absent. The highest component in the expansion (2.10) possesses the maximal U(1) charge L It is a descendant of the lowest weight vector. For the low boundary m − m = 1, the eigenstate Ψα has a unit U(1) charge and, it is given by a linear combination of θ’s with prefactors depending on z−variables only The latter are fixed from the requirement that Ψα has to be annihilated by the lowering generators yielding.
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