Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A formula on $g=1$ quantum K-invariants

Dun Tang

Abstract

In this paper, we prove an analog of Dijkgraaf-Witten's theorem for $g=1$ invariants in quantum K-theory.

A formula on $g=1$ quantum K-invariants

Abstract

In this paper, we prove an analog of Dijkgraaf-Witten's theorem for invariants in quantum K-theory.

Paper Structure

This paper contains 11 sections, 9 theorems, 86 equations.

Table of Contents

  1. Proof of Theorem 1
  2. Example: $\left<\frac{1}{1-q_1 L}, \frac{1}{1-q_2L}\right>_{1,2}$ of point target space
  3. Preparations
  4. Computations via Theorem 1
  5. Contributions from $F_1(\tau)$
  6. Contributions from $\frac{1}{24}\log \frac{\partial \tau}{\partial t_0}$
  7. Contributions from $n=0$ term in $F^{tw}_1(\bar{\mathbf{t}}^{new})-F^{tw}_1(\bar{\mathbf{t}}^{fake})$
  8. Contributions from $n=1$ term in $F^{tw}_1(\bar{\mathbf{t}}^{new})$
  9. Contributions from $n=1$ term in $F^{tw}_1(\bar{\mathbf{t}}^{fake})$
  10. Comparing the results
  11. $1$-pointed $g=1$ invariants of the point target space

Key Result

Theorem 1

The no-permutation invariant is Where $F_1(\tau) = \mathcal{F}_1(\tau)$ is the $g=1$ primary invariants.

Theorems & Definitions (16)

  • Theorem 1
  • Proposition 1.1
  • Lemma 1.1
  • proof
  • proof
  • Theorem 2
  • Lemma 3.1
  • proof
  • proof
  • Proposition 3.1
  • ...and 6 more