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Anomaly cancellation and modularity: E8*E8*E8 case

Siyao Liu, Yong Wang, Yuchen Yang

Abstract

In [5] and [19], the authors gave anomaly cancellation formulas for the gauge groups E8,E8*E8. In this paper, we mainly deal with the case of gauge group E8*E8*E8. Using the E8*E8*E8 bundle, we construct some modular forms over SL2(Z). By these modular forms, we get some new anomaly cancellation formulas of characteristic forms.

Anomaly cancellation and modularity: E8*E8*E8 case

Abstract

In [5] and [19], the authors gave anomaly cancellation formulas for the gauge groups E8,E8*E8. In this paper, we mainly deal with the case of gauge group E8*E8*E8. Using the E8*E8*E8 bundle, we construct some modular forms over SL2(Z). By these modular forms, we get some new anomaly cancellation formulas of characteristic forms.
Paper Structure (8 sections, 15 theorems, 76 equations)

This paper contains 8 sections, 15 theorems, 76 equations.

Table of Contents

  1. Introduction
  2. The basic knowledge
  3. Anomaly cancellation formulas
  4. Anomaly cancellation formulas for the gauge group $E_{8}$
  5. Anomaly cancellation formulas for the gauge group $E_{8}\times E_{8}$
  6. Anomaly cancellation formulas for the gauge group $E_{8}\times E_{8}\times E_{8}$
  7. Conclusion
  8. Acknowledgements

Key Result

Lemma 3.1

$Q_{1}(Z, \tau)$ is a modular form of weight $10$ over $SL_{2}(\mathbf{Z}).$

Theorems & Definitions (26)

  • Definition 2.1
  • Lemma 3.1
  • proof
  • Theorem 3.2
  • proof
  • Lemma 3.3
  • Lemma 3.4
  • proof
  • Theorem 3.5
  • proof
  • ...and 16 more