Stefanski, B. & Tseytlin, A. A. (2005). Super spin chain coherent state actions and $AdS_5 \times S^5$ superstring. Nuclear Physics B, 718(12), pp. 83112. doi: 10.1016/j.nuclphysb.2005.04.026

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Abstract
We consider a generalization of the leadingorder matching of coherent state actions for semiclassical states on the super YangMills and the superstring sides of the AdS/CFT duality to sectors with fermions. In particular, we discuss the $SU(11)$ and $SU(23)$ 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 $SU(23)$ 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 ``LandauLifshitz'' form as the action in the bosonic SU(3) sector with the target space $CP^2$ replaced by the projective superspace $CP^{22}$. We then attempt to relate it to the corresponding truncation of the full $AdS_5 \times S^5$ superstring action written in a lightcone gauge where it has simple quartic fermionic structure. In particular, we find that part of the superstring action describing $SU(11)$ sector reduces to an action of a massive twodimensional relativistic fermion, with the expansion in the effective coupling $\lambda/J^2$ being equivalent to a nonrelativistic expansion.
Item Type:  Article 

Subjects:  Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
Related URLs:  
URI:  http://openaccess.city.ac.uk/id/eprint/1023 
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