论文标题
拓扑对称的Orbifold
The Topological Symmetric Orbifold
论文作者
论文摘要
我们通过利用数学文献来分析有关复杂表面M的对称产物的拓扑轨道共形田间理论。我们表明，操作员环的规范商具有Hurwitz数字给出的结构常数。这证明了有关极端相关因子的物理文献中的猜想。此外，它允许利用对称组的组合制剂的结果明确计算更多的结构常数。我们记得，完全的Orbifold手性环由对称的Orbifold Frobenius代数给出。该构建可以计算零属和一个相关属，并证明较高属的贡献消失。对所有拓扑相关器的有效描述为拓扑广告/CFT对应关系的证明设定了阶段。的确，我们提出了证明的具体数学化身，将大量的gromow-witten理论与边界上希尔伯特方案的量子共同体相关。
We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by Hurwitz numbers. This proves a conjecture in the physics literature on extremal correlators. Moreover, it allows to leverage results on the combinatorics of the symmetric group to compute more structure constants explicitly. We recall that the full orbifold chiral ring is given by a symmetric orbifold Frobenius algebra. This construction enables the computation of topological genus zero and genus one correlators, and to prove the vanishing of higher genus contributions. The efficient description of all topological correlators sets the stage for a proof of a topological AdS/CFT correspondence. Indeed, we propose a concrete mathematical incarnation of the proof, relating Gromow-Witten theory in the bulk to the quantum cohomology of the Hilbert scheme on the boundary.
