2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183037We derive the coherent state representation of the integrable spin chain Hamiltonian with supersymmetry group $SU(1,1|2)$. By the use of a projected Hamiltonian onto bosonic states, we give explicitly the action of the Hamiltonian on $SU(2)\times SL(2)$ coherent states. Passing to the continuous limit, we find that the corresponding bosonic sigma model is the sum of the known SU(2) and SL(2) ones, and thus it gives a string spinning fast on $S^1_{ϕ_1}\times S^1_{ϕ_1}\times S^1_{ϕ_2}$ in $\rm{AdS}_5 \times S^5$. The full sigma model on the supercoset $SU(1,1|2)/SU(1|1)^2$ is given.20 pages, no figures, 4 tables, 1 appendix; typos corrected, references addedHigh Energy Physics - Theorytext