Classical/quantum integrability in non-compact sector of AdS/CFT

By Vladimir Kazakov, K. Zarembo. 2004

224 citations recorded by the source corpus.

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5521e7a860b4ca1e75563cd5846605e243e3397f

How researchers see this paper

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

In Geometry and Topology

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

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

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

Citations in the corpus

• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, background): “20) with the finite-gap integral equations of [44, 45] we should start with their unscaled form14”
• Spinning strings in AdS5 × S5: one-loop correction to energy in SL(2) sector (2005, methodology): “In particular, the spin chain Bethe ansatz and the string theory computations of the subleading 1/J corrections are not directly related: while the Bethe ansatz approach does reproduce part of the spectrum of the bosonic string fluctuations near a given semiclassical solution [5, 28],(3) the string ”
• On integrability of classical superstrings in AdS5 × S5 (2005, background): “To derive the classical Bethe equations describing the finite-gap solutions of the string sigma-model [21, 23] one has to investigate the asymptotic properties of the Lax connection and the associated monodromy around the regular points λ = 0 and λ = ∞.”
• Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, background): “In the following we will be interested only in the first type of deformation.”
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal (2008, methodology): “We will consider a class of solutions of (71), with the one-cut solution of [42] particularly in mind, vis-à-vis those of the analogous sl(2) Bethe equation in AdS5×S(5) to which it has a great degree of similarity.”
• Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings (2005, methodology): “An approximate stringy S-matrix was obtained for sl(2) from a discretization of the finite gap equation describing the classical sigma model in this sector [10].”
• The Algebraic Curve of Classical Superstrings on AdS5×S5 (2005, background): “Likewise, the involved group manifolds are considered to be universal coverings.”
• Complete spectrum of long operators in N=4 SYM at one loop (2005, methodology): “tacks of negative grading η k = η l = −1 (k,l = 1,2,7,8) are associated to the non-compact su(2,2)-part of the su(2,2|4)-algebra. They form strings stretching along the real axis of the complex plane [44]. • Fermionic stacks which have mixed grading η k 6= η l (k = 3,4,5,6 and l = 1,2,7,8 or vice ve”
• Algebraic Curve for the SO(6) Sector of AdS/CFT (2004, unknown): “ar X ∗Membre de l’Institut Universitaire de France”
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT (2006, background): “As was shown in [10] (see also [17]), the leading h1 term here is reproduced as the corresponding term in the 1-loop anomalous dimension on the gauge theory side, implying its non-renormalizability as one goes from weak to strong coupling in the above large charge limit.”
• Integrable Hamiltonian for Classical Strings on AdS5 x S5 (2004, methodology): “For strings moving in R × S3, AdS3 × S1 and R × S5 they were derived in [ 7 ].”
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory (2015, background): “As such, the computation of the so-called stochastic anomaly is the same as at weak coupling and we can simply plug the strong coupling quasi-momenta [54] in the final result (3.”