Super spin chain coherent state actions and image superstring Original Research Article

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 image and image sectors containing states with angular momentum J in image and spin in image. On the SYM side, we start with the dilatation operator in the image 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 image sector with the target space image replaced by the projective superspace image. We also discuss the complete image one-loop SYM spin chain coherent state sigma model action. We then attempt to relate it to the corresponding truncation of the full image 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 image sector reduces to an action of a massive 2d relativistic fermion, with the expansion in the effective coupling image being equivalent to a non-relativistic expansion.