Super spin chain coherent state actions and AdS5×S5 superstring

We consider a generalization of leading-order matching of coherent state actions for semiclassical states on the super-Yang-Mills and superstring sides of the AdS/CFT duality to sectors with fermions. In particular, we discuss the SU(1|1) and SU(2|3) sectors containing states with angular momentum J in S5 and spin in AdS5. On the SYM side, we start with the dilatation operator in the SU(2|3) sector having super spin chain Hamiltonian interpretation and derive the corresponding coherent state action which is quartic in fermions. This action has essentially the same “Landau-Lifshitz” form as the action in the bosonic SU(3) sector with the target space CP2 replaced by the projective superspace CP2|2. We also discuss the complete PSU(2,2|4) one-loop SYM spin chain coherent state sigma model action. We then attempt to relate it to the corresponding truncation of the full AdS5×S5 superstring action written in a light-cone gauge where it has simple quartic fermionic structure. In particular, we find that part of the superstring action describing SU(1|1) sector reduces to an action of a massive 2d relativistic fermion, with the expansion in the effective coupling λ˜=λJ2 being equivalent to a non-relativistic expansion.