Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry

Yongbin Ruan; Yaoxiong Wen; Zijun Zhou

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arXiv · 2011.07519

Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry

Yongbin Ruan·Yaoxiong Wen·Zijun Zhou

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Abstract

We introduce a new version of 3d mirror symmetry for toric stacks, inspired by a 3d $\mathcal{N} = 2$ abelian mirror symmetry construction in physics. Given some toric data, we introduce the $K$-theoretic $I$-function with effective level structure for the associated toric stack. When a particular stability condition is chosen, it restricts to the $I$-function for the particular toric GIT quotient. The mirror of a toric stack is defined by the Gale dual of the original toric data. We then proved the mirror conjecture that the $I$-functions of a mirror pair coincide, under the mirror map, which switches K\"ahler and equivariant parameters, and maps $q\mapsto q^{-1}$.

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BibTeX RIS

Yongbin Ruan, Yaoxiong Wen, Zijun Zhou. 2020-11-15. Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry. https://arxiv.org/abs/2011.07519

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