论文标题
量子歧管上的Yang-Mills连接和Sigma-Models
Yang-Mills connections and sigma-models on quantum Heisenberg manifolds
论文作者
论文摘要
我们在Heisenberg歧管上构建了光谱三重，该量子概括了Chakraborty和Shinha的结果，并遵循Mathai-Rosenberg对非线性Sigma模型的方法，与它相关。我们构造的光谱三元延伸扩展了我们为此能量功能提供的下限，该功能与投影的拓扑电荷相关，这取决于兼容连接的曲率。对量子海森堡歧管中的康投影进行了对这种下限的详细研究。这些结果表现出与量子海森贝格歧管的非线性sigma模型与杨米尔斯理论之间的有趣相互作用，这与未经共同的Tori的情况不同。
We construct a spectral triple on a quantum Heisenberg manifold, which generalizes the results of Chakraborty and Shinha, and associate to it an energy functional on the set of projections, following the approach of Mathai-Rosenberg to non-linear sigma models. The spectral triples that we construct extend the We derive a lower bound for this energy functional that is linked on the topological charge of the projection which depends on the curvature of a compatible connection. A detailed study of this lower bound is given for the Kang projection in quantum Heisenberg manifolds. These results display an intriguing interplay between non-linear sigma models and Yang-Mills theory on quantum Heisenberg manifolds, unlike in the well-studied case of noncommutative tori.
