Superstring action inAdS5×S5:κ-symmetry light cone gauge

As part of a program to quantize superstrings in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ in a light-cone gauge we find the explicit form of the corresponding Green-Schwarz action in the fermionic light-cone $\kappa$-symmetry gauge. The resulting action contains terms quadratic and quartic in fermions. In the flat space limit it reduces to the standard light-cone GS action, while for ${\alpha }^{\prime }\to 0$ it has the correct ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ light-cone superparticle limit. We discuss fixing the bosonic light-cone gauge and a reformulation of the action in terms of 2D Dirac spinors.