String hypothesis for gl(n|m) spin chains: a particle/hole democracy

TL;DR

This paper develops a string hypothesis for gl(n|m) spin chains, deriving functional equations that symmetrically treat particles and holes, and connects these to the Y-system to understand the model's symmetry and excitations.

Contribution

It introduces a novel string hypothesis framework for gl(n|m) spin chains, linking functional equations to the Y-system and symmetry analysis, extending previous results to new models.

Findings

Derived linear functional equations for particles and holes

Mapped the Y-system to symmetry properties of the model

Generalized results to AdS/CFT and Hubbard model contexts

Abstract

This paper is devoted to integrable gl(n|m) spin chains which allow for formulation of the string hypothesis. Considering the thermodynamic limit of such spin chains, we derive linear functional equations that symmetricaly treat holes and particles. The functional equations naturally organize different types of excitations into a pattern equivalent to the one of Y-system, and, not surprisingly, the Y-system can be easily derived from the functional equations. The Y-system is known to contain most of the information about the symmetry of the model, therefore we map the symmetry knowledge directly to the description of string excitations. Our analysis is applicable for highest weight representations which for some choice of the Kac-Dynkin diagram have only one nonzero Dynkin label. This generalizes known results for the AdS/CFT spectral problem and for the Hubbard model.