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

TL;DR

This paper develops the theory of levels in quantum K-theory, establishing toric mirror theorems with applications, and uncovers connections to Ramanujan's mock theta functions in simple examples.

Contribution

It introduces the concept of levels in quantum K-theory and proves mirror theorems for permutation-equivariant cases, revealing unexpected links to mock theta functions.

Findings

Toric mirror theorems for quantum K-theory with level structure

Emergence of Ramanujan's mock theta functions in examples

Foundation for further development of quantum K-theory levels

Abstract

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 toric 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.