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

TL;DR

This work advances the quantum string description in AdS5×S5 by formulating an exact uniform light-cone gauge action and Hamiltonian, enabling a controlled near-plane-wave expansion to compute 1/J corrections in rank-1 subsectors. It demonstrates the existence of perturbative, dilatation-like effective Hamiltonians for closed sectors and introduces a compact set of light-cone Bethe equations that reproduce correct strong-coupling and spinning-string limits without a dressing factor at leading order. The analysis provides a concrete link between the string spectrum and gauge-theory integrability in a gauge-fixed, perturbative setting, and lays out a program for extending these results to higher orders, winding sectors, and the full PSU(2,2|4) structure. Overall, the paper offers a coherent framework to study quantum string spectra via light-cone methods and Bethe equations, with implications for the AdS/CFT correspondence and integrability in string theory.

Abstract

We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green-Schwarz superstring in AdS5xS5. 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 N=4 gauge theory.