Duality between Supergravity and Gauge Theories and Supersymmetry Breaking

1.我们推广了5维AdS超引力理论和4维规范理论之间的AdS/CFT对应。我们已经展示了如何超越1/N领先近似。我们证明了Weyl反常中的1/N^2项可以用Wheeler-De Witt方程的技巧在引力扇区中重现.在超对称性破缺的异常调解方案中，我们解决了长期以来所知的所谓的超光速粒子问题。指出在计算中不仅要考虑Weyl反常项，而且要考虑Kaehler反常项。我们提出了一个唯象可行的模型，解决了超光速子问题.我们分析了非对易空间中的低维场论。在非对易标量场论中构造了孤子解，并充分阐明了孤子的模等性质。在非对易空间中构造了一类新的非线性sigma模型，并分析了其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与规范理论之间对偶性的理解.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Einstein-Yamg-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，这种配置可能与早期宇宙中的剩余磁场有关。我们也做了一些与高能唯象学密切相关的工作。作为研究额外维度物理的产物，我们计算了双轻子的产生截面。这是基于希格斯场不是一个内置场，而是额外维度紧化的结果。我们还计算了量子电动力学和弱电辐射修正的中微子相关的反应，如那些在KamLAND和SNO。

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.