Feynman Graph Integrals and Almost Modular Forms

Abstract

We introduce a type of graph integrals on elliptic curves from the heat kernel. We show that such graph integrals have modular properties under the modular group $SL(2,\mathbb{Z})$, and prove the polynomial nature of the anti-holomorphic dependence.

26 pages

References in corpus (2)

• Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
• Topological Strings and (Almost) Modular Forms

Cited by in corpus (2)

• Ramanujan Identities and Quasi-Modularity in Gromov-Witten Theory
• Renormalization Method and Mirror Symmetry