$K$-theoretic quasimap wall-crossing

Ming Zhang; Yang Zhou

$K$-theoretic quasimap wall-crossing

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arxiv 2012.01401 v1 pith:PJ5HXMYF submitted 2020-12-02 math.AG math-phmath.MP

Ming Zhang , Yang Zhou This is my paper · ORCID

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keywords k-theoreticgenus-0mirrortheoremwall-crossingarxivauthorepsilon

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abstract

In this paper, we prove a K-theoretic wall-crossing formula for $\epsilon$-stable quasimaps for all GIT targets in all genera. It recovers the genus-0 K-theoretic toric mirror theorem by Givental-Tonita and the genus-0 mirror theorem for quantum K-theory with level structure by Ruan-Zhang. The proofs are based on K-theoretic virtual localization on the master space introduced by the second author in arXiv:1911.02745.

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Quantum K-theory levels in physics and math
hep-th 2025-06 conditional novelty 6.0 of 10

Chern-Simons levels and Ruan-Zhang levels are identified as the same twisting of quantum K-theory, with Coulomb branch equations matching difference operator symbols and geometric windows matching mirror triviality.

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