We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS 5 × S 5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N = 4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant λ, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives λ ≈ 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model. *

We feel really honoured to give a talk before active researchers in this frontier field of physics, gauge theory and gravity. Although the member of our group are not familiar with the details of concepts and theoretical approachs in this field, we understand the importance of the Aharonov-Bohm effect in the electromagnetism, i.e. the first example of gauge fields. I) 2)-4) Since the theoretical work by Aharonov and Bohm in 1959, several experiments have been performed to prove this effect and these experiments have been fairly famous also among electron-microscopist.We thought the effect has the sound basis beyond doubt but we noticed also that a few people5)still insisted on its non-existance or doubted the validity of the experiments and that the controversy still continued. 6j' Therefore it seemed worth while to try an experiment in a newly designed form to confirm the effect again. This was our motivation.Before going into our experiment, let us explain briefly about those in the past.The schematic diagram in Fig.l shows the idea of the elaborate experiment by M~llenstedt group. 2} ' The lens and bi-prism are, of cource, electro-magnetic ones in fact. They fabricated a fine solenoid coil whose diameter was unbelievably small, 4.7 pm.Two electron waves from the same source travel around the solenoid and are overlapped coherently to cause interference fringes on the film below. Even if the waves never touch the magnetic flux inside the solenoid, the fringe must be shifted with the change in the phase difference between the waves owing to the Aharonov-Bohm effect when the coil current ~ changes. In order to confirm the fringe shift, they set a slit over the recoreding film and moved the film with changing the coil current i.The result is reproduced in Fig.2. The fringe shift is clearly recorded.'3j-4Lre~ " sl i art Other experiments a "m'l o this one in principle except that ferromagnetic needles were used instead of solenoids.All these experiments were very elaborate ones for the technology of those days but we must admit that they have one defect in common. That is, the lack of experimental verifications that there is no magnetic flux leakage into the electron paths.To improve this points, Kuper7)proposed in 1980 the idea of perfect confinement of magnetic fluxon by a hollow torus of super-conductive material, as shown in Fig.3.

We study a family of classical string solutions with large spins on R t S 3 subspace of AdS 5 S 5 background, which are related to Complex sine-Gordon solitons via Pohlmeyer's reduction. The equations of motion for the classical strings are cast into Lamé equations and Complex sine-Gordon equations. We solve them under periodic boundary conditions, and obtain analytic profiles for the closed strings. They interpolate two kinds of known rigid configurations with two spins: on one hand, they reduce to folded or circular spinning/rotating strings in the limit where a soliton velocity goes to zero, while on the other hand, the dyonic giant magnons are reproduced in the limit where the period of a kink-array goes to infinity.

No abstract