The non-semisimple Verlinde formula and pseudo-trace functions
The non-semisimple Verlinde formula and pseudo-trace functions
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DOI：
10.1016/j.jpaa.2018.04.014
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发表时间：
2016-05
影响因子：
0.8
通讯作者：
A. Gainutdinov;A. Gainutdinov;I. Runkel
中科院分区：
文献类型：
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作者：
A. Gainutdinov;A. Gainutdinov;I. Runkel
利用Shimizu关于内字符的结果，我们证明了可分解有限张量范畴的范畴Verlinde公式的一个有用的非半简单变体。从推测上讲，这种范畴的例子由顶点算子代数V在一定有限条件下的表示形式Rep V给出。结合Miyamoto和Arike-Nagatomo关于伪迹函数的结果，可以对V的伪迹函数的模性质与Rep V的Grothendieck环上的积之间的非半单模Verlinde公式作出一个精确的猜想。我们通过显式计算伪迹函数的模s变换，以N对辛费米子的顶点算子代数为例验证了这一猜想。
Using results of Shimizu on internal characters we prove a useful non-semisimple variant of the categorical Verlinde formula for factorisable finite tensor categories. Conjecturally, examples of such categories are given by the representations Rep V of a vertex operator algebra V subject to certain finiteness conditions. Combining this with results on pseudo-trace functions by Miyamoto and Arike–Nagatomo, one can make a precise conjecture for a non-semisimple modular Verlinde formula which relates modular properties of pseudo-trace functions for V and the product in the Grothendieck ring of Rep V. We test this conjecture in the example of the vertex operator algebra of N pairs of symplectic fermions by explicitly computing the modular S-transformation of the pseudo-trace functions.