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We consider classical superstrings propagating on AdS_5 x S^5 space-time. Weconsistently truncate the superstring equations of motion to the so-calledsu(1|1) sector. By fixing the uniform gauge we show that physical excitationsin this sector are described by two complex fermionic degrees of freedom and weobtain the corresponding Lagrangian. Remarkably, this Lagrangian can be cast ina two-dimensional Lorentz-invariant form. The kinetic part of the Lagrangianinduces a non-trivial Poisson structure while the Hamiltonian is just the oneof the massive Dirac fermion. We find a change of variables which brings thePoisson structure to the canonical form but makes the Hamiltonian nontrivial.The Hamiltonian is derived as an exact function of two parameters: the totalS^5 angular momentum J and string tension \lambda; it is a polynomial in 1/Jand in \sqrt{\lambda'} where \lambda'=\frac{\lambda}{J^2} is the effective BMNcoupling. We identify the string states dual to the gauge theory operators fromthe closed su(1|1) sector of N=4 SYM and show that the corresponding near-planewave energy shift computed from our Hamiltonian perfectly agrees with thatrecently found in the literature. Finally we show that the Hamiltonian isintegrable by explicitly constructing the corresponding Lax representation.Comment: 35 pages;v2:typos corrected, references adde

New integrable system of 2dim fermions from strings on AdS5× S5

New integrable system of 2dim fermions from strings on AdS₅× S⁵