J. Luis Miramontes

An integrable deformation of the AdS5×S5superstring

The S-matrix on the world-sheet theory of the string in AdS has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where q is real has been identified as a particular deformation of the Green–Schwarz sigma model. An interpretation of the case with q a root of unity has, until now, been lacking. We show that the Green–Schwarz sigma model admits a discrete deformation which can be viewed as a rather simple deformation of the gauged WZW model, where . The deformation parameter q is then a kth root of unity where k is the level. The deformed theory has the same equations-of-motion as the Green–Schwarz sigma model but has a different symplectic structure. We show that the resulting theory is integrable and has just the right amount of kappa-symmetries that appear as a remnant of the fermionic part of the original gauge symmetry. This points to the existence of a fully consistent deformed string background.

The symmetric space and homogeneous sine-Gordon theories

Two series of integrable theories are constructed which have soliton solutions and can be thought of as generalizations of the sine-Gordon theory. They exhibit internal symmetries and can be described as gauged WZW theories with a potential term. The spectrum of massive states is determined.

Integrable deformations of strings on symmetric spaces

A bstractA general class of deformations of integrable sigma-models with symmetric space F/G target-spaces are found. These deformations involve defining the non-abelian T dual of the sigma-model and then replacing the coupling of the Lagrange multiplier imposing flatness with a gauged F/F WZW model. The original sigma-model is obtained in the limit of large level. The resulting deformed theories are shown to preserve both integrability and the equations-of-motion, but involve a deformation of the symplectic structure. It is shown that this deformed symplectic structure involves a linear combination of the original Poisson bracket and a generalization of the Faddeev-Reshetikhin Poisson bracket which we show can be re-expressed as two decoupled F current algebras. It is then shown that the deformation can be incorporated into the classical model of strings on ℝ×F/G

q-deformation of the AdS5 × S5 superstring S-matrix and its relativistic limit

\mathbb{R}\times F/G

Restoring unitarity in the q-deformed world-sheet S-matrix

via a generalization of the Pohlmeyer reduction. In this case, in the limit of large sigma-model coupling it is shown that the theory becomes the relativistic symmetric space sine-Gordon theory. These results point to the existence of a deformation of this kind for the full Green-Schwarz superstring on AdS5 × S5.

Bound states of the q-deformed AdS5×S5 superstring S-matrix

A systematic group theoretical formulation of the Pohlmeyer reduction is presented. It provides a map between the equations of motion of sigma models with target-space a symmetric space = F/G and a class of integrable multi-component generalizations of the sine-Gordon equation. When is of definite signature their solutions describe classical bosonic string configurations on the curved space-time t × . In contrast, if is of indefinite signature the solutions to those equations can describe bosonic string configurations on t × , × S1 or simply . The conditions required to enable the Lagrangian formulation of the resulting equations in terms of gauged WZW actions with a potential term are clarified, and it is shown that the corresponding Lagrangian action is not unique in general. The Pohlmeyer reductions of sigma models on Pn and AdSn are discussed as particular examples of symmetric spaces of definite and indefinite signature, respectively.

The AdS5 × S5 semi-symmetric space sine-Gordon theory

A bstractA set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

\mathfrak{s}\mathfrak{u}\left( {2|2} \right)