# The level structure in quantum K-theory and mock theta functions

@article{Ruan2018TheLS, title={The level structure in quantum K-theory and mock theta functions}, author={Yongbin Ruan and Ming Ming Zhang}, journal={arXiv: Algebraic Geometry}, year={2018} }

This is the first in a sequence of papers to develop the theory of levels in quantum K-theory and study its applications. Our main results in this paper are mirror theorems for permutation-equivariant quantum K-theory with level structure. In some of the simplest examples, we see the surprising appearance of Ramanujan's mock theta functions.

## 21 Citations

Quantum K-theory of Calabi-Yau manifolds

- MathematicsJournal of High Energy Physics
- 2019

Abstract
The disk partition function of certain 3d N = 2 supersymmetric gauge theories computes a quantum K-theoretic ring for Kähler manifolds X. We study the 3d gauge theory/quantum K-theory…

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- 2021

This is a set of lecture notes for the first author’s lectures on the difference equations in 2019 at the Institute of Advanced Study for Mathematics at Zhejiang University. We focus on explicit…

BPS Indices, Modularity and Perturbations in Quantum K-theory

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- 2021

We study a perturbation family of N = 2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator–Vafa formula is given for the quantum K-theory ring of Grassmannians.…

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- 2019

Given a smooth, complex projective variety X, one can associate to it numerical invariants by taking holomorphic Euler characteristics of natural vector bundles on the moduli spaces of stable maps to…

Quantum K-theory of flag varieties via non-abelian localization

- Mathematics
- 2021

We provide an explicit parameterization (a.k.a. ”reconstruction”) of the permutationinvariant big J -function of partial flag varieties, treated as a non-abelian GIT quotient of a linear space, by…

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- Mathematics
- 2018

The 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kahler manifold X, which is reproduced in the IR limit. We propose and explore a 3d lift of this correspondence,…

Quantum Kirwan for quantum K-theory

- Mathematics
- 2019

For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory QK^G(X) to…

K-Theoretic $I$-function of $V//_{\theta} \mathbf{G}$ and Application

- Mathematics
- 2019

In this paper, we compute K-theoretic $I$-function with level structure (defined by quasi-map theory) of GIT-quotient of a vector space via abelian and non-abelian correspondence. As a consequence,…

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