After the two years ago work of Seiberg and Witten [1, 2], the Pandora box of string theory has been opened once more. The magic opening word has been duality. A web of exciting interrelated results it contains has appeared during the last months: string-string duality (U duality) [3]; the physical interpretation of the conifold singularity [4]; heterotic-type II dual pairs [3, 5, 6, 7, 8]; R-R...

We present a simple procedure to construct non-local conserved charges for classical open strings on coset spaces. This is done by including suitable reflection matrices on the classical transfer matrix. The reflection matrices must obey certain conditions for the charges to be conserved and in involution. We then study bosonic open strings on AdS5×S. We consider boundary conditions correspondi...

On this note we prove that a holomorphic foliation of the projective plane with rich, but finite, automorphism group does not have invariant algebraic curves.

We derive the two-loop Bethe ansatz for the sl(2) twist operator sector of N = 4 gauge theory directly from the field theory. We then analyze a recently proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large spacetime spin at large but finite twist, and find a novel all-loop scaling function. This function obeys the Kotikov-Lipatov transcendentality principle and does not ...

The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are polynomial in momenta one can construct a corresponding commuting set of differential operators. Here we discuss some 2or 3-dimensional purely quantum integrab...

Abstract We present a special issue reviewing various topics that include: classical and quantum integrability, integrable deformations, the 4D Chern–Simons theory, double field theory α ′ ...

A number of interesting problems can be modeled with nonlinear differential-difference equations (DDEs) [1][3], including particle vibrations in lattices, currents in electrical networks, and pulses in biological chains. Nonlinear DDEs also play a role in queuing problems and discretizations in solid state and quantum physics, and arise in the numerical solution of nonlinear PDEs. The study of ...