Duality between Supergravity and Gauge Theories and Supersymmetry Breaking

1.推广了5维ADS-超重力与4维ADS/CFT的对应关系。规范理论。我们已经展示了如何超越1/N前导近似。我们证明了利用Wheeler-de Witt方程的技术，Weyl异常中的1/N^2项可以在引力扇区中重现。我们解决了在超对称破裂的异常调解场景中已知已久的所谓的超速粒子问题。我们指出，不仅要考虑Weyl反常项，还要考虑Kaehler反常项。我们提出了一个现象学上可行的模型，在该模型中已经解决了快子受扰问题。我们分析了非对易空间中的低维场理论。我们在非对易标量场论中构造了孤子解，并充分阐明了模等孤子的性质。在非对易空间中构造了一种新型的非线性Sigma模型，并对模型的因果关系和能量条件进行了分析。这些研究将有助于我们进一步深化对引力理论和规范理论之间的二元性的理解。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。我们发现了爱因斯坦-Yamg-Mills理论中规范场的一种新的经典构型。我们指出，这种构型可能与早期宇宙中的剩余磁场有一定的关联。我们还做了一些与高能现象学密切相关的工作。作为超维物理研究的一个成果，我们计算了双轻子的产生截面。这是基于这样一种观点，即希格斯场不是内置场，而是额外维度压缩的结果。我们还计算了与中微子有关的反应的QED和电弱辐射修正，如卡姆兰德和SNO中的反应。

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.