N=4 SYM to Two Loops: Compact Expressions for the Non-Compact Symmetry Algebra of the su(1,1|2) Sector

We begin a study of higher-loop corrections to the dilatation generator of N=4 SYM in non-compact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higher-loop corrections. Remarkably, we find a short and simple expression for the two-loop dilatation generator. Our solution for the non-compact su(1,1|2) sector consists of nested commutators of four O(g) generators and one simple auxiliary generator. Moreover, the solution does not require the planar limit; we conjecture that it is valid for any gauge group. To obtain the two-loop dilatation generator, we find the complete O(g^3) symmetry algebra for this sector, which is also given by concise expressions. We check our solution using published results of direct field theory calculations. By applying the expression for the two-loop dilatation generator to compute selected anomalous dimensions and the bosonic sl(2) sector internal S-matrix, we confirm recent conjectures of the higher-loop Bethe ansatz of hep-th/0412188.Comment: 28 pages, v2: additional checks against direct field theory calculations, references added, minor corrections, v3: additional minor correction

Nonobstructing Colonic Dilatation and Colon Perforations Following Renal Transplantation

Nonobstructing colonic dilatation has not been commonly reported following renal transplantation, and colon perforations carry a high morbidity and mortality in this population. During a 7-year period, nonobstructing colonic dilatation developed in 13 adults 1 to 13 days after renal transplantation. Twelve (92%) of the 13 had poorly functioning allografts. Five (83%) of the 6 with and 2 (29%) of the 7 without colonoscopy had resolution of nonobstructing colonic dilatation. Of the seven right-sided colon perforations during this period, six were associated with nonobstructing colonic dilatation. An additional 4 patients had diverticular perforations in the left colon. Of a total of 11 patients with colon perforation, 7 had surgery within 24 hours of the perforation and 6 (86%) of these survived. Only 1 (25%) of the 4 having surgery more than 24 hours later survived. Six of the survivors retained functioning allografts. Nonobstructing colonic dilatation seems to be a potential complication of poor graft function after renal transplantation, and colonoscopy is effective in its treatment. In patients with colon perforations, early surgery and reduced immunosuppression are essential in decreasing mortality. © 1990, American Medical Association. All rights reserved