The Algebraic Curve of Classical Superstrings on AdS5×S5

By N. Beisert, Vladimir Kazakov, Kazuhiro Sakai, K. Zarembo. 2005

347 citations recorded by the source corpus.

We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS5×S5. 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 supersymmetric gauge theory proving the complete agreement of spectra in this approximation.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ba71051fc6bb13ed89e5714897cfff4e400d6e5c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. S. Frolov
2. A. Tseytlin
3. G. Arutyunov
4. N. Beisert
5. Romuald A. Janik
6. R. Roiban
7. K. Zarembo
8. M. Staudacher

In Nuclear and High Energy Physics

1. S. Frolov
2. G. Arutyunov
3. N. Beisert
4. A. Tseytlin
5. R. Roiban
6. Romuald A. Janik
7. M. Staudacher
8. L. Alday

Citations in the corpus

• The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “One of the most fascinating discoveries in recent years was the unravelling of integrable structures in planar N = 4 SYM [1, 2, 3, 4] and in superstring theory on AdS5 × S(5) [5, 6, 7, 8, 9, 10, 11].”
• B-field in AdS3/CF T2 correspondence and integrability (2012, background): “This is useful, for example, in the construction of the algebraic curve for the classical solutions of the sigma-model [32].”
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, background): “Integrability on the string side has been established at the level of the classical theory, where again an infinite set of conserved charges may be constructed [5, 11].”
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “From this they conjectured the finite size correction coming both from the modification of the Bethe Ansatz and from the effect of the sea of particles and anti-particles.”
• Uniform Light-Cone Gauge for Strings in AdS5 x S5: Solving su(1|1) Sector (2005, background): “In fact the whole classical (finite-gap) spectrum is encoded into a set of certain integral (Bethe type) equations [11] supported on the corresponding algebraic curves [12].”
• Four loop twist two, BFKL, wrapping and strings (2008, background): “The Bethe Ansatz Equations have been derived [12, 13, 14, 15, 16, 17, 18, 19] giving the spectrum of states with large quantum numbers.”
• Green-Schwarz Strings in TsT-transformed backgrounds (2005, methodology): “It would be interesting to analyze the properties of the monodromy matrix and derive finite-gap integral equations for the deformed model analogous to those derived for strings in AdS5 × S5 in [30, 28].”