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E8 bundles and some new anomaly cancellation formulas

Yong Wang

Abstract

Using $E_8$ bundles, we construct some new modular forms over $SL(2,{\bf Z})$, $Γ^0(2)$ and $Γ_0(2)$ and get some new anomaly cancellation formulas of characteristic forms which generalize some anomaly cancellation formulas in [13].

E8 bundles and some new anomaly cancellation formulas

Abstract

Using bundles, we construct some new modular forms over , and and get some new anomaly cancellation formulas of characteristic forms which generalize some anomaly cancellation formulas in [13].
Paper Structure (4 sections, 28 theorems, 88 equations)

This paper contains 4 sections, 28 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. $SL(2,Z)$ modular forms and anomaly cancellation formulas for $14$ and $10$-dimensional $spin^c$ manifolds
  3. $\Gamma^0(2)$ modular forms and anomaly cancellation formulas for $14$ and $10$-dimensional $spin^c$ manifolds
  4. Acknowledgements

Key Result

Lemma 2.2

$Q(M,P_i,P_j,V,\tau)$ is a modular form over $SL_2({\bf Z})$ with the weight $14$.

Theorems & Definitions (30)

  • Definition 2.1
  • Lemma 2.2
  • Theorem 2.3
  • Corollary 2.4
  • Lemma 2.5
  • Theorem 2.6
  • Corollary 2.7
  • Lemma 2.8
  • Theorem 2.9
  • Corollary 2.10
  • ...and 20 more