The Baxter Q-operatorfor the graded SL(2|1) spin chain

Abstract

We study an integrable non-compact superspin chain model that emerged in recent studiesof the dilatation operator in the super-Yang–Mills theory. It was found that the latter can be mappedinto a homogeneous Heisenberg magnet with the quantum space inall sites corresponding to infinite dimensional representations of theSL(2|1) group. We extend themethod of the Baxter Q-operator to spin chains with supergroup symmetry and apply it to determine theeigenspectrum of the model. Our analysis relies on a factorization property of the -operators acting on the tensor product of two generic infinite dimensionalSL(2|1) representations. It allows us to factorize an arbitrary transfer matrix intoa product of three ‘elementary’ transfer matrices which we identify as BaxterQ-operators. We establish functional relations between transfer matrices and use them to derive theT–Q relationsfor the Q-operators. The proposed construction can be generalized to integrable models based onsupergroups of higher rank and, as distinct from the Bethe ansatz, it is not sensitive tothe existence of the pseudovacuum state in the quantum space of the model.