论文标题
Anyonic缺陷括号和扭曲的模化差异（TED）K理论中的保形块
Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
论文作者
论文摘要
我们证明，横向复杂曲线的扭曲的模化差异K理论可容纳codimension = 2个缺陷麸皮形式的外来电荷，例如iib/f理论的A-type orbifold奇异性的D7-溴化物的d7-棕褐色，同时又有其双重3-辅助术的三体性缺陷。在F理论和AGT对应关系中，这些麸皮被争辩，以携带特殊的SL（2） - 单骨home术的指控，但其他麸皮未见，但以前在K理论给出的预期的Brane电荷量化定律中都没有确定这些指控。 Here we observe that it is the subtle (and previously somewhat neglected) twisting of equivariant K-theory by flat complex line bundles appearing inside orbi-singularities ("inner local systems") that makes the secondary Chern character on a punctured plane inside an A-type singularity evaluate to the twisted holomorphic de Rham cohomology which Feigin, Schechtman & Varchenko showed realizes SL（2，c） - 符号块，在1度中 - 实际上，它在所有可接受的分数级别上都提供了这些块的直接总和。如果我们假设先前讨论过关于M理论中的勃雷电荷量化的“假设h”，则其余的高度共形块也会出现类似的外观。 Since conformal blocks -- and hence these twisted equivariant secondary Chern characters -- solve the Knizhnik-Zamolodchikov equation and thus constitute representations of the braid group of motions of defect branes inside their transverse space, this provides a concrete first-principles realization of anyon statistics of -- and hence of topological quantum computation on -- defect branes in string/M-theory.
We demonstrate that twisted equivariant differential K-theory of transverse complex curves accommodates exotic charges of the form expected of codimension=2 defect branes, such as of D7-branes in IIB/F-theory on A-type orbifold singularities, but also of their dual 3-brane defects of class-S theories on M5-branes. These branes have been argued, within F-theory and the AGT correspondence, to carry special SL(2)-monodromy charges not seen for other branes, but none of these had previously been identified in the expected brane charge quantization law given by K-theory. Here we observe that it is the subtle (and previously somewhat neglected) twisting of equivariant K-theory by flat complex line bundles appearing inside orbi-singularities ("inner local systems") that makes the secondary Chern character on a punctured plane inside an A-type singularity evaluate to the twisted holomorphic de Rham cohomology which Feigin, Schechtman & Varchenko showed realizes sl(2,C)-conformal blocks, here in degree 1 -- in fact it gives the direct sum of these over all admissible fractional levels. The remaining higher-degree conformal blocks appear similarly if we assume our previously discussed "Hypothesis H" about brane charge quantization in M-theory. Since conformal blocks -- and hence these twisted equivariant secondary Chern characters -- solve the Knizhnik-Zamolodchikov equation and thus constitute representations of the braid group of motions of defect branes inside their transverse space, this provides a concrete first-principles realization of anyon statistics of -- and hence of topological quantum computation on -- defect branes in string/M-theory.
