We compute the elliptic genus for arbitrary two dimensional $N=2$Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs ofsuch models. We show that if two Landau-Ginzburg models are conjugate to eachother in a certain sense, then to every orbifold of the first theorycorresponds an orbifold of the second theory with the same elliptic genus (upto a sign) and with the roles of the chiral and anti-chiral rings interchanged.These orbifolds thus constitute a possible mirror pair. Furthermore, new pairsof conjugate models may be obtained by taking the product of old ones. We alsogive a sufficient (and possibly necessary) condition for two models to beconjugate, and show that it is satisfied by the mirror pairs proposed by one ofthe authors and~H\"ubsch.
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机译：我们为任意二维$ N = 2 $ Landau-Ginzburg Orbifolds计算椭圆族。这用于搜索此类模型的可能镜像对。我们表明，如果两个Landau-Ginzburg模型在某种意义上彼此共轭，则第一个理论的每个等价点对应于第二个理论的同一个椭圆属（直到一个符号），并且具有手性和反手性环互换，因此这些圆环构成了可能的镜像对。此外，可以通过取旧模型的乘积来获得新的共轭模型对。我们还给出了两个模型要共轭的充分（可能必要）条件，并表明作者之一和Hübsch提出的镜像对满足它。
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