Minimal surfaces in AdS space and integrable systems

Abstract

We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS₅. The Lax pair for the reduced theory is found, and written entirely in terms of the A₃ = D₃ root system, generalizing the B₂ affine Toda system which appears for the AdS₄ string. For the B₂ affine Toda system, we show that the area of the worlsheet is obtainable from the moduli space Kähler potential of a related Hitchin system. We also explore the Saveliev-Leznov construction for solutions of the B₂ affine Toda system, and recover the rotationally symmetric solution associated to Painleve transcendent.