Communications in Number Theory and Physics

Volume 9 (2015)

Number 4

Elliptic genera of Berglund–Hübsch Landau–Ginzburg orbifolds

Pages: 741 – 761



Minxian Zhu (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)


We match the elliptic genus of a Berglund–Hübsch Landau–Ginzburg orbifold with the supertrace of $y^{J[0]} q^{L[0]}$ on a vertex algebra $V_{1,1}$. We show that it is a weak Jacobi form and the elliptic genus of one theory is equal (up to a sign) to the elliptic genus of its mirror.

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