Quantum AdS5 × S5 superstring in the AdS light-cone gauge

We consider the AdS 5 × S 5 superstring in the light-cone gauge adapted to a massless geodesic in AdS 5 in the Poincaré patch. The resulting action has a relatively simple structure which makes it a natural starting point for various perturbative quantum computations. We illustrate the utility of this AdS light-cone gauge action by computing the 1-loop and 2-loop corrections to the null cusp anomalous dimension reproducing in a much simpler and efficient way earlier results obtained in conformal gauge. This leads to a further insight into the structure of the superstring partition function in non-trivial background.