Scattering amplitudes at strong coupling for 4K gluons

In this paper we study the scattering amplitudes at strong coupling for the case where the number of gluons is a multiple of four. This is an important missing piece in arXiv:1002.2459. The tricky point for n=4K is that there is some accidental degeneracy in such case. We explain this point in detail and show that a non-trivial monodromy around infinity was developed by the world-sheet coordinate transformation appearing in the computation. It turns out that besides solving the Y system, we also need to calculate T functions to compute the full amplitudes. We show that the T functions can be derived by taking a limit of Y functions of a higher-point case. As a check, we obtain the known result of eight-point in AdS_3 case.Comment: 23 pages, 3 figures. v3: A major revision of the paper, various points much clarified, appendix added; no change of the main result

On Cotorsion pairs of chain complexes

In the paper we first construct a new cotorsion pair, in the category of chain complexes, from two given cotorsion pairs in the category of modules, and then we consider completeness of such pairs under certain conditions.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1210.0196 by other author