Minimal surfaces in AdS space and Integrable systems

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.

30 pages, JHEP style; v2, minor changes; v3, minor changes, version published in JHEP.

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Cited by in corpus (10)

• T-systems and Y-systems in integrable systems
• Space-like minimal surfaces in AdS x S
• ODE/IM correspondence and modified affine Toda field equations
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• General Leznov-Savelev solutions for Pohlmeyer reduced AdS${}_5$ minimal surfaces
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Novel aspects of integrability for NLSMs in symmetric spaces
• A short review on TBA equation and scattering amplitude/Wilson loop duality