Interpolating families of integrable AdS3 backgrounds

We construct families of integrable deformations that interpolate between AdS3 × S3× S3 × S1 and either AdS3 × S3 × S2 × T2 or AdS3 × S2 × S2 × T3 . They preserve half of the supersymmetry of the original background, namely one copy of the d ( 2 , 1 ; α ) algebra. From this it follows a similar integrable interpolation between AdS3 × S3 × T4 and AdS3 × S2 × T5 , which also preserves half of the supersymmetry, namely a copy of the psu ( 1 , 1 | 2 ) algebra. In all cases, the interpolating backgrounds are constructed by using TsT transformations, which makes it easy to implement them in the integrability formalism in the full quantum theory. To illustrate this point, we discuss the lightcone gauge fixing of the models and compute their pp-wave Hamiltonian.