Abstract In this paper, by defining a new vocabulary for Jacobi theta functions, namely “spectral theta functions”, we show that how remarkably the N = 2 superconformal characters are extracted by imposing a residue calculation on s l ( 2 | 1 ) affine Lie superalgebra characters in their non-unitary (non-trivial) cases. Therefore, to have more versatility in conformal quantum field theory context, we finalize our study by a complete prescription by which, all contents of well-known s l ( 2 | 1 ) characters could be uniquely translated to N = 2 superconformal characters. In this regard, we firstly establish the key spectral theta function’s formula as well as deriving quasi-periodic and differentiation formulae of spectral theta functions. Then, both the mentioned algebraic characters in their non-unitary cases are studied to explore a relation between these algebras. Finally we come up with our residue calculation method to obtain a total reduction from s l ( 2 | 1 ) characters to N = 2 characters, as a novel and applicable idea in mathematical physics.

中文翻译：

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N=2 超共形字符作为 sl̂(2|1) 仿射李超代数字符的残差，通过为 Jacobi theta 函数定义一个新词汇表

摘要 在本文中，通过为 Jacobi theta 函数定义一个新的词汇，即“谱 theta 函数”，我们展示了通过对 sl ( 2 | 1 ) 仿射李超代数进行残差计算来提取 N = 2 个超共形字符的显着性字符在其非单一（非平凡）情况下。因此，为了在共形量子场论上下文中具有更多的通用性，我们通过一个完整的处方来完成我们的研究，通过该处方，众所周知的 sl ( 2 | 1 ) 字符的所有内容都可以唯一地转换为 N = 2 个超共形字符。对此，我们首先建立了关键的谱θ函数公式，并推导了谱θ函数的准周期和微分公式。然后，研究了它们非幺正情况中提到的两个代数字符，以探索这些代数之间的关系。最后，我们提出了我们的残差计算方法，以获得从 sl ( 2 | 1 ) 个字符到 N = 2 个字符的总减少，作为数学物理中一个新颖且适用的想法。