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arXiv · 0911.4551

Minimal surfaces in AdS space and Integrable systems

Benjamin A. Burrington·Peng Gao
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Abstract

We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS$_5$. The Lax pair for the reduced theory is found, and written entirely in terms of the $A_3=D_3$ root system, generalizing the $B_2$ affine Toda system which appears for the AdS$_4$ string. For the $B_2$ 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 $B_2$ affine Toda system, and recover the rotationally symmetric solution associated to Painleve transcendent.

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Benjamin A. Burrington, Peng Gao. 2010-03-30. Minimal surfaces in AdS space and Integrable systems. https://doi.org/10.1007/jhep04(2010)060

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