New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5

We consider classical superstrings propagating on AdS_5 x S^5 space-time. We consistently truncate the superstring equations of motion to the so-called su(1|1) sector. By fixing the uniform gauge we show that physical excitations in this sector are described by two complex fermionic degrees of freedom and we obtain the corresponding Lagrangian. Remarkably, this Lagrangian can be cast in a two-dimensional Lorentz-invariant form. The kinetic part of the Lagrangian induces a non-trivial Poisson structure while the Hamiltonian is just the one of the massive Dirac fermion. We find a change of variables which brings the Poisson structure to the canonical form but makes the Hamiltonian nontrivial. The Hamiltonian is derived as an exact function of two parameters: the total S^5 angular momentum J and string tension \lambda; it is a polynomial in 1/J and in \sqrt{\lambda'} where \lambda'=\frac{\lambda}J^2 is the effective BMN coupling. We identify the string states dual to the gauge theory operators from the closed su(1|1) sector of N=4 SYM and show that the corresponding near-plane wave energy shift computed from our Hamiltonian perfectly agrees with that recently found in the literature. Finally we show that the Hamiltonian is integrable by explicitly constructing the corresponding Lax representation.

Reviewed papers on Pith that cite this one. The full citation record

1. Bethe Ansatz in Stringy Sigma Models hep-th · Mar 2006
2. The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry hep-th · Mar 2006
3. Superstrings on AdS_4 x CP^3 as a Coset Sigma-model hep-th · Jun 2008
4. On String S-matrix, Bound States and TBA hep-th · Oct 2007
5. The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations hep-th · Mar 2006
6. TTbar deformation and the light-cone gauge hep-th · May 2019
7. Integrable S matrix, mirror TBA and spectrum for the stringy $\text{AdS}_{3}\times\text{S}^3\times\text{S}^3\times\text{S}^1$ WZW model hep-th · Dec 2018
8. Twisting the Mirror TBA hep-th · Sep 2010
9. Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3 hep-th · Jul 2008
10. The S-matrix of String Bound States hep-th · Mar 2008
11. The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring hep-th · Dec 2006
12. The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring hep-th · Sep 2006
13. Finite-size Effects from Giant Magnons hep-th · Jun 2006
14. On AdS_5 x S^5 String S-matrix hep-th · Apr 2006
15. Green-Schwarz Strings in TsT-transformed backgrounds hep-th · Dec 2005
16. Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector hep-th · Oct 2005
17. Wrapping interactions and a new source of corrections to the spin-chain/string duality hep-th · Oct 2005
18. $T{\overline T}$, $\widetilde JJ$, $JT$ and $\widetilde JT$ deformations hep-th · Jul 2019
19. The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5 hep-th · Apr 2006
20. On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory hep-th · Mar 2006
21. Foundations of the AdS_5 x S^5 Superstring. Part I hep-th · Jan 2009
22. Integrability of the AdS_5 x S^5 superstring and its deformations hep-th · Oct 2013