Duality between Supergravity and Gauge Theories and Supersymmetry Breaking

1. 我们扩展了5-dim AdS-超重力和4-dim AdS/CFT对应关系。计理论。我们已经展示了如何超越1/N前导近似。我们已经证明了Weyl异常中的1/N^2项可以用Wheeler-De Witt方程的技术在引力扇区重现。我们解决了超光速破环的异常调解场景中存在已久的所谓速子睡眠问题。指出除了weyl异常项外，还应考虑Kaehler异常项。我们提出了一个现象学上可行的模型，该模型解决了速子睡眠问题。分析了非交换空间中的低维场论。在非对易标量场理论中构造了孤子解，充分阐明了孤子的模等性质。在非交换空间中构造了一种新型的非线性sigma模型，并分析了因果关系和能量条件。这些研究将有助于进一步加深我们对引力理论和规范理论对偶性的认识。作为上述研究的副产品，我们将规范理论和引力理论应用于早期宇宙理论。我们在爱因斯坦-杨-米尔斯理论中发现了规范场的一种新的经典构型。我们指出，这种结构可能与早期宇宙的残余磁场有关。我们还做了一些与高能现象学密切相关的工作。作为研究超维物理的成果，我们计算了双光子的产生截面。这是基于希格斯场不是一个内置场，而是作为额外维度紧化的结果而产生的想法。我们还计算了卡姆兰和SNO等中微子相关反应的QED和电弱辐射校正。

1. We have extended the AdS/CFT correspondences between 5-dim AdS-supergravity and 4-dim. gauge theories. We have shown how to go beyond the 1/N leading approximation. We have demonstrated the 1/N^2 terms in Weyl Anomaly can be reproduced in the gravitational sector by using the technique of the Wheeler-De Witt equation.2. We attacked the so-called tachyonic slepton problem known for long time in the anomaly mediation scenario of SUSY breaking. We pointed out that not only the Weyl-anomaly terms but also Kaehler anomaly should be taken into account. We proposed a phenomenologically viable model, in which tachyonic slepton problem has been solved.3. We analyzed low dimensional field theories in noncommutative space. We constructed soliton solutions in noncommutative scalar field theories and properties of solitons such as moduli have been fully clarified. We also constructed new-type of non-linear sigma model in non-commutative space and causality and energy-conditions are analyzed. These researches will be helpful for further deepning of our understanding of the duality between gravity and gauge theories.4. As byproducts of the above research, we applied the gauge and gravitational theories to the theory of early universe. We discovered a new classical configurartion of gauge fields in the Einstein-Yamg-Mills theory. We pointed out that this configuration might have some relevance to the residual magnetic filed in the early universe.5. We have also done some works which have closely related to high energy phenomenology. As a product of investigating physics of extra-dimensions, we have calculated the production cross section of bileptons. This is based on the idea that Higgs field is not a built-in field but comes out as a consequence of compactification of extra dimensions. We have also calculated to QED and electroweak radiative corrections to neutrino related reactions such as those in KamLAND and SNO.