Journal
ADVANCES IN MATHEMATICS
Volume 410, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2022.108770
Keywords
3d mirror symmetry; Quantum K-theory; Level structure
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Funding
- KIAS Individual Grant [MG083901]
- Korea Institute for Advanced Study
- POSCO Science fellowship
- World Premier International Research Center Initiative (WPI) , MEXT, Japan
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This paper introduces a new version of 3d mirror symmetry for the toric quotient stack [Cn/K], which is inspired by a 3d N = 2 abelian mirror symmetry construction in physics. The paper proves the mirror conjecture that the I-functions of a mirror pair coincide under the mirror map.
We introduce a new version of 3d mirror symmetry for the toric quotient stack [Cn/K] where K = (C*)k and the torus action is determined by the given charge matrix. It is inspired by a 3d N = 2 abelian mirror symmetry construction in physics. Given some toric data, we introduce the K-theoretic I-function with the effective level structure for the associated quotient stack. When a particular stability condition is chosen, it restricts to the I-function for the particular toric variety. The mirror of a GIT quotient stack is defined by the Gale dual of the original toric data. We then prove the mirror conjecture that the I-functions of a mirror pair coincide, under the mirror map, which switches Kahler and equivariant parameters, and changes q to q-1. (c) 2022 Elsevier Inc. All rights reserved.
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