The Algebraic Curve of Classical Superstrings on AdS 5×S 5

2005/02/28 by Niklas Beisert, N. Beisert, Vladimir Kazakov +5 · 291 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic number #Black Holes and Theoretical Physics #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Superstring theory #hep-th #nlin.SI

paper · pdf · doi:10.1007/s00220-006-1529-4

published in Communications in Mathematical Physics 263(3), 659-710 (Springer Science+Business Media) · 56 pages, v2: first local charge derived, minor improvements, references added, v3: minor corrections, reference added, to appear in Commun. Math. Phys

arxiv created 2005/10/03 · openalex publication_date 2006/03/03 · arxiv updated 2011/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS₅xS⁵. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar, one-loop N=4 supersymmetric gauge theory proving the complete agreement of spectra in this approximation.

Citations

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