We consider Jordanian deformations of the AdS 5 ×S 5 superstring action. These deformations correspond to non-standard q-deformations. In particular, it is possible to perform a partial deformation, for example, of the AdS 5 part only, or of the S 5 part only. Then the classical action and the Lax pair are constructed with a linear, twisted and extended R operator. It is shown that the action preserves the κ-symmetry.

Bone remodeling, comprising resorption of existing bone and de novo bone formation, is required for the maintenance of a constant bone mass. Prostaglandin (PG)E 2 promotes both bone resorption and bone formation. By infusing PGE 2 to mice lacking each of four PGE receptor (EP) subtypes, we have identified EP4 as the receptor that mediates bone formation in response to this agent. Consistently, bone formation was induced in wild-type mice by infusion of an EP4-selective agonist and not agonists specific for other EP subtypes. In culture of bone marrow cells from wild-type mice, PGE2 induced expression of core-binding factor ␣1 (Runx2͞Cbfa1) and enhanced formation of mineralized nodules, both of which were absent in the culture of cells from EP4-deficient mice. Furthermore, administration of the EP4 agonist restored bone mass and strength normally lost in rats subjected to ovariectomy or immobilization. Histomorphometric analysis revealed that the EP4 agonist induced significant increases in the volume of cancellous bone, osteoid formation, and the number of osteoblasts in the affected bone of immobilized rats, indicating that activation of EP4 induces de novo bone formation. In addition, osteoclasts were found on the increased bone surface at a density comparable to that found in the bone of control animals. These results suggest that activation of EP4 induces bone remodeling in vivo and that EP4-selective drugs may be beneficial in humans with osteoporosis.B ones undergo continuous remodeling through repeated cycles of destruction and rebuilding (1). This remodeling is mediated by the well balanced actions of osteoclasts, which resorb old bones, and osteoblasts, which form new bones. However, in the elderly, especially in postmenopausal women, the extent of bone resorption far exceeds that of bone rebuilding, resulting in osteoporosis and the associated increases in bone fragility and susceptibility to fractures (2). About 100 million people are estimated to suffer from this debilitating disease worldwide. Several drugs have been developed to treat osteoporosis, with most inhibiting bone resorption and only a few promoting bone formation (3). Such modulation of only one of the two processes in bone remodeling renders these drugs of limited efficacy in restoring the normal balance and bone mass.Recently, significant advances have been made in our understanding of molecular mechanisms of osteoclast and osteoblast differentiation (4), but such knowledge has not been exploited fully to develop a drug that corrects the imbalance and restores normal bone remodeling. Prostaglandins (PGs) are a group of lipid mediators that are produced from arachidonic acid in a variety of tissues under various physiological and pathophysiological conditions and serve to maintain local homeostasis (5). Among them, PGs of the E type work bimodally in bone metabolism (6). PGE 2 potently induces bone resorption in bone organ cultures, whereas repeated injection of this compound in vivo induces bone formation in a variety of animals includ...

Abstract:We consider γ-deformations of the AdS 5 ×S 5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real γ-deformations of the AdS 5 ×S 5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.

Abstract:We derive the gravity duals of noncommutative gauge theories from the YangBaxter sigma model description of the AdS 5 ×S 5 superstring with classical r-matrices. The corresponding classical r-matrices are 1) solutions of the classical Yang-Baxter equation (CYBE), 2) skew-symmetric, 3) nilpotent and 4) abelian. Hence these should be called abelian Jordanian deformations. As a result, the gravity duals are shown to be integrable deformations of AdS 5 ×S 5 . Then, abelian twists of AdS 5 are also investigated. These results provide a support for the gravity/CYBE correspondence proposed in arXiv:1404.1838.