Sigma model from SU(1,1|2)SU(1,1|2) spin chain

We derive the coherent state representation of the integrable spin chain Hamiltonian with supersymmetry group SU(1,1|2)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)×SL(2)SU(2)×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)SU(2) and SL(2)SL(2) ones, and thus it gives a string spinning fast on Sϕ11×Sφ11×Sφ21 in AdS5×S5AdS5×S5. The full sigma model on the supercoset SU(1,1|2)/SU(1|1)2SU(1,1|2)/SU(1|1)2 is given.