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Anomaly cancellation formulas and E_8 bundles for almost complex manifolds

Siyao Liu, Yong Wang

Abstract

In this paper, we extend the elliptic genus in [10] by the gauge group E_8 and the gauge group E_8*E_8. Then we prove that the generalized elliptic genus are the weak Jacobi forms. Using these elliptic genus, we obtain some SL_2(Z) modular forms and get some new anomaly cancellation formulas of characteristic forms for almost complex manifolds.

Anomaly cancellation formulas and E_8 bundles for almost complex manifolds

Abstract

In this paper, we extend the elliptic genus in [10] by the gauge group E_8 and the gauge group E_8*E_8. Then we prove that the generalized elliptic genus are the weak Jacobi forms. Using these elliptic genus, we obtain some SL_2(Z) modular forms and get some new anomaly cancellation formulas of characteristic forms for almost complex manifolds.
Paper Structure (5 sections, 12 theorems, 115 equations)

This paper contains 5 sections, 12 theorems, 115 equations.

Table of Contents

  1. Introduction
  2. The generalized elliptic genus
  3. Anomaly cancellation formulas for the gauge group $E_{8}$
  4. Anomaly cancellation formulas for the gauge group $E_{8}\times E_{8}$
  5. Acknowledgements

Key Result

Lemma 2.1

(GBL) A holomorphic function $\phi(\tau, z):\mathcal{H}\times \mathcal{C}\rightarrow\mathcal{C}$ is called a weak Jacobi form of weight $k\in\mathbf{Z}/2$ and index $t\in\mathbf{Z}/2$ if it satisfies the functional equations and where $\mathcal{C}$ is the complex plane.

Theorems & Definitions (19)

  • Lemma 2.1
  • Definition 2.2
  • Lemma 2.3
  • Theorem 2.4
  • proof
  • Definition 2.5
  • Lemma 2.6
  • Theorem 2.7
  • proof
  • Lemma 3.1
  • ...and 9 more