The classical exchange algebra of a Green-Schwarz sigma model on supercoset target space with $\mathbb {Z}_{4m}$Z4m grading

Abstract

We investigate the classical exchange algebra of the monodromy matrix for a Green-Schwarz sigma model on supercoset target space with $\mathbb {Z}_{4m}$Z4m grading by using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution in the Poisson bracket sense. Our calculation is based on a general world-sheet metric. Taking a particular case of m = 1 (and a particular choice of supergroup), our results coincide with those of the Green-Schwarz superstring theory in AdS5 × S5 background obtained by Magro [J. High Energy Phys. 0901, 021 (2009)]10.1088/1126-6708/2009/01/021.