Superparticle and superstring in AdS3×S3 Ramond–Ramond background in the light-cone gauge

We discuss superparticle and superstring dynamics in ${\mathrm{AdS}}_3{\mathrm{\times S}}^3$ supported by R–R 3-form background using light-cone gauge approach. Starting with the superalgebra $\mathrm{psu}\text{(1,1|2)⊕}\mathrm{psu}\mathrm{\sim }\text{(1,1|2)}$ representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near ${\mathrm{AdS}}_3{\mathrm{\times S}}^3$ background and thus the corresponding Kaluza–Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green–Schwarz ${\mathrm{AdS}}_3{\mathrm{\times S}}^3$ superstring action and find the corresponding light-cone string Hamiltonian. We also obtain a realization of the generators of $\mathrm{psu}\text{(1,1|2)⊕}\mathrm{psu}\mathrm{\sim }\text{(1,1|2)}$ in terms of the superstring 2-d fields in the light-cone gauge.