Nonrelativistic expansion of Green-Schwarz strings on $Ad{S}_5\times S^5$

We perform nonrelativistic expansions of type IIB $Ad{S}_5\times S^5$ Green-Schwarz (GS) superstrings upto quadratic order in fermionic excitation. We carry out a systematic $1\mathrm{/}c$ expansion both for the bosonic as well as the fermionic sector of the type IIB model and explore the LO theory in detail. We explore various global as well as local symmetries of the nonrelativistic sigma model at LO including the world-sheet supersymmetry. As a special case, we choose the flat gauge and explore the longitudinal T-duality rules for the LO theory. Finally, we comment on the NLO theory and some interesting properties of it.