Sergey Frolov

We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green-Schwarz superstring in AdS5xS5. We then quantize the theory perturbatively in the near plane-wave limit, and compute the leading 1/J correction to a generic string state from the rank-1 subsectors. These investigations enable us to propose a new set of light-cone Bethe equations for the quantum string. The equations have a simple form and yield the correct spinning string and flat space limits. Finally, we clarify the notion of closed sectors in string theory by proving the existence of perturbative effective string Hamiltonians which are direct analogues of (all loop) dilatation operators in the dual N=4 gauge theory.

Recently two interesting conjectures about the string S-matrix on AdS_5 x S^5 have been made. First, assuming the existence of a Hopf algebra symmetry Janik derived a functional equation for the dressing factor of the quantum string Bethe ansatz. Second, Hernandez and Lopez proposed an explicit form of 1/\sqrt\lambda correction to the dressing factor. In this note we show that in the strong coupling expansion Janik's equation is solved by the dressing factor up to the order of its validity. This observation provides a strong evidence in favor of a conjectured Hopf algebra symmetry for strings in AdS_5 x S^5 as well as the perturbative string S-matrix.

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial background in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted boundary conditions. Our construction implies that a TsT transformation preserves integrability properties of the string sigma model. We discuss in detail type IIB strings propagating in the \g_i-deformed AdS_5 x S^5 space-time, find the twisted boundary conditions for bosons and fermions, and use them to write down an explicit expression for the monodromy matrix. We also discuss string zero modes whose dynamics is governed by a fermionicgeneralization of the integrable Neumann model.

We introduce a uniform light-cone gauge for strings propagating in AdS space-time. We use the gauge to analyze strings from the su(1|1) sector, and show that the reduced model is described by a quadratic action for two complex fermions. Thus, the uniform light-cone gauge allows us to solve the model exactly. We analyze the near BMN spectrum of states from the su(1|1) sector and show that it correctly reproduces the 1/J corrections. We also compute the spectrum in the strong coupling limit, and derive the famous \lambda^{1/4} asymptotics. We then show that the same string spectrum can be also derived by solving Bethe ansatz type equations, and discuss their relation to the quantum string Bethe ansatz for the su(1|1) sector.

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.

We consider a non-supersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS_5 x S5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters gamma_i which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N=4 SYM theory, but with scalar and Yukawa interactions ``deformed'' by gamma_i-dependent phases. The special case of equal deformation parameters gamma_i=gamma corresponds to the N=1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal gamma_i this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective ``Landau-Lifshitz'' actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e. it allows one to capture the right vacuum states and the macroscopic spin wave sector of states of the spin chain in the continuum coherent state effective action.