标题： 从模糊球面量子卡拉布-克莱因模型得到的杨-米尔斯场 显示英文标题

标题： Yang-Mills field from fuzzy sphere quantum Kaluza-Klein model

摘要： 使用量子黎曼几何的框架，我们证明在最小假设下，时空与模糊球面的乘积上的引力等价于时空上的引力，一个取值于$su_2$的杨-米尔斯场$A_{\mu i}$以及一个取值于实对称矩阵的Liouville-σ模型场$h_{ij}$，用于模糊球面上的引力。 此外，乘积上的无质量实标量场表现为时空上的标量场族，每个内部整数自旋$l$表示的$SU(2)$都有一个，与$A_{\mu i}$最小耦合，并且质量取决于$l$和模糊球面的大小。 对于变形参数的离散值，模糊球可以简化为矩阵代数$M_{2j+1}(C)$，其中$j$为任何非负半整数，在这种情况下，多重态中仅出现整数自旋$0\le l\le 2j$。 因此，对于$j=1$，乘积上的无质量场表现为无质量的$SU(2)$内部自旋 0 场、有质量的内部自旋 1 场和有质量的内部自旋 2 场，其质量比分别为$0,1,\sqrt{3}$，我们推测这可能与近似的$SU(2)$额外对称性有关。 显示英文摘要

摘要： Using the framework of quantum Riemannian geometry, we show that gravity on the product of spacetime and a fuzzy sphere is equivalent under minimal assumptions to gravity on spacetime, an $su_2$-valued Yang-Mills field $A_{\mu i}$ and real-symmetric-matrix valued Liouville-sigma model field $h_{ij}$ for gravity on the fuzzy sphere. Moreover, a massless real scalar field on the product appears as a tower of scalar fields on spacetime, with one for each internal integer spin $l$ representation of $SU(2)$, minimally coupled to $A_{\mu i}$ and with mass depending on $l$ and the fuzzy sphere size. For discrete values of the deformation parameter, the fuzzy spheres can be reduced to matrix algebras $M_{2j+1}(C)$ for $j$ any non-negative half-integer, and in this case only integer spins $0\le l\le 2j$ appear in the multiplet. Thus, for $j=1$ a massless field on the product appears as a massless $SU(2)$ internal spin 0 field, a massive internal spin 1 field and a massive internal spin 2 field, in mass ratio $0,1,\sqrt{3}$ respectively, which we conjecture could arise in connection with an approximate $SU(2)$ flavour symmetry.