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We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS_5xS^5. 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.
We explore integrability properties of superstring equations of motion in AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding Hamiltonian dynamics on subspace of physi
We construct the general algebraic curve of degree four solving the classical sigma model on RxS5. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N=4 SYM, also constructed here. We explicitly reproduce some particular solutions.
The classical spectral curve for the worldsheet theory of the AdS_5 x S^5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T dual of the AdS_5 x S^5 superstring with respect to full PSU(2,2|4) symmetry
Motivated by the notorious difficulties in determining the first quantum corrections to the spectrum of short strings in AdS_5xS^5 from first principles, we study closed bosonic strings in this background employing a static gauge. In this gauge the w
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 d