• Corpus ID: 119636853

# 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}
}
• Published 18 April 2018
• Mathematics
• arXiv: Algebraic Geometry
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.
Quantum K theory of symplectic Grassmannians
• Mathematics
Journal of Geometry and Physics
• 2022
Quantum K-theory of Calabi-Yau manifolds
• Mathematics
Journal 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
Quantum $K$-theory and $q$-Difference equations
• Mathematics
• 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
• Mathematics
• 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.
Quantum K-Theory with Level Structure
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
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
A 3d gauge theory/quantum K-theory correspondence
• 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
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,

## References

SHOWING 1-10 OF 59 REFERENCES
Quantum $K$-theory, I: Foundations
This work is devoted to the study of the foundations of quantum K-theory, a K-theoretic version of quantum cohomology theory. In particular, it gives a deformation of the ordinary K-ring K(X) of a
On the WDVV equation in quantum K-theory.
0. Introduction. Quantum cohomology theory can be described in general words as intersection theory in spaces of holomorphic curves in a given Kahler or almost Kahler manifold X. By quantum K-theory
Permutation-equivariant quantum K-theory VI. Mirrors
We present here the K-theoretic version of mirror models of toric manifold. First, we recall the construction of cohomological mirrors for toric manifolds, i.e. representations of the toric
Permutation-equivariant quantum K-theory VII. General theory
We introduce K-theoretic GW-invariants of mixed nature: permutation-equivariant in some of the inputs and ordinary in the others, and prove the ancestor-descendant correspondence formula. In genus 0,
Topological Mirrors and Quantum Rings
Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities
Baxter Q-operator from quantum K-theory
• Mathematics