论文标题
在精致的Chern-simons /拓扑弦上二元性二元性方面
On refined Chern-Simons / topological string duality for classical gauge groups
论文作者
论文摘要
我们以任意A，B，C，D仪表代数在$ s^3 $上介绍了精致的Chern-Simons理论的分区函数。对于B和C案例，此表示是新颖的。它使我们能够猜测二元性对已解决的Conifold上的拓扑字符串的一些精致和定向的版本，并对不同贡献进行详细识别。 D和C代数的自由能具有A理论，即可定向表面的一半贡献，以及具有一个交叉表的不可定向表面的贡献，具有相反的符号，类似于未精制理论。但是，在精制的情况下，这两种理论都具有与两个交叉杯的可定向表面的非零贡献。特别是，我们观察到Kähler参数的特里布尔，从改进和世界表（即交叉杯数）依赖的量子变化的意义上。对于b代数，克莱因瓶的贡献为零，与未精制理论一样，一折叠的术语与d和c案例不同。对于这些理论的（精制）恒定地图术语，我们建议模块化不变的表示，从而导致自然拓扑的解释。我们还计算了一些非扰动校正。
We present the partition function of the refined Chern-Simons theory on $S^3$ with arbitrary A,B,C,D gauge algebra in terms of multiple sine functions. For B and C cases this representation is novel. It allows us to conjecture duality to some refined and orientifolded versions of the topological string on the resolved conifold, and carry out the detailed identification of different contributions. The free energies for D and C algebras possess the usual halved contribution from the A theory, i.e. orientable surfaces, and contributions of non-orientable surfaces with one cross-cup, with opposite signs, similar as for the non-refined theories. However, in the refined case, both theories possess in addition a non-zero contribution of orientable surfaces with two cross-cups. In particular, we observe a trebling of the Kähler parameter, in the sense of a refinement and world-sheet (i.e. the number of cross-cups) dependent quantum shift. For B algebra the contribution of Klein bottles is zero, as is the case in the non-refined theory, and the one-cross-cup terms differ from the D and C cases. For the (refined) constant maps terms of these theories we suggest a modular-invariant representation, which leads to natural topological string interpretation. We also calculate some non-perturbative corrections.
