Super spin chain coherent state actions and [formula omitted] superstring

Abstract

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 S 5 and spin in AdS 5 . 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 C P 2 replaced by the projective superspace C P 2 | 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 AdS 5 × S 5 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 ˜ = λ J 2 being equivalent to a non-relativistic expansion.