The AdS₅xS⁵ Superstring in Light-Cone Gauge and its Bethe Equations

We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green–Schwarz superstring in AdS5 × S5. We then quantize the theory perturbatively in the near plane wave limit, and compute the leading 1/J correction to a generic string state from the rank-1 subsectors. These investigations enable us to propose a new set of light-cone Bethe equations for the quantum string. The equations have a simple form and yield the correct spinning string and flat space limits. Finally, we clarify the notion of closed sectors in string theory by proving the existence of perturbative effective string Hamiltonians which are direct analogues of (all-loop) dilatation operators in the dual {\cal N}=4 gauge theory