We find a family of solutions to Zamolodchikov's tetrahedral algebra corresponding to the fermionic R-operator for the free fermion model of the difference type in one of the spectral parameters, construct an extension of the R-operator for a system of two spins satisfying the Yang-Baxter equation, and find the local charges. We also construct a twisted monodromy operator, which leads to the one-dimensional Hubbard model.
In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access previously unreachable quantities such as correlation functions at finite coupling. In the setup of 1D defect CFT living on a Maldacena-Wilson line, we managed to compute with good precision a non-supersymmetric structure constant for a wide range of the `t Hooft coupling. Our result is particularly precise at strong coupling and matches well with the recent analyt…
In the framework of six-dimensional conformal field theories with ${\cal N}=(1,0)$ supersymmetry we develop the map between the holographic description, the field theoretical description and the associated Hanany-Witten set-ups. General expressions that calculate various observables are presented. The study of string solitons singles out a special background of Massive IIA on which we show (by explicitly finding a Lax pair) that the Neveu-Schwarz part of the string sigma model is classically integrable. We study the particular dual conformal field theory and compute some of its observables.
We show that the tree dimensional Einstein vacuum field equations with cosmological constant are integrable. Using the $sl(2,R)$ valued soliton connections we obtain the metric of the spacetime in terms of the dynamical variables of the integrable nonlinear partial differential equations.
We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization…
Bäcklund-type transformations in four-dimensional space-time and an intriguing reduced zero-curvature formulation for axially symmetric membranes, with diffeomorphism-, resp. Lorentz-, symmetries reappearing after orthonormal gauge-fixing, are found.
