Modular forms and hierarchical Yukawa couplings in heterotic Calabi-Yau compactifications

Understand

We study the modular symmetry in heterotic string theory on Calabi-Yau threefolds.

• In particular, we examine whether moduli-dependent holomorphic Yukawa couplings are described by modular forms in the context of heterotic string theory with standard embedding.
• We find that $SL(2,\mathbb{Z})$ modular symmetry emerges in asymptotic regions of the Calabi-Yau moduli space.
• The instanton-corrected holomorphic Yukawa couplings are then given by modular forms under $SL(2,\mathbb{Z})$ or its congruence subgroups such as $\Gamma_0(3)$ and $\Gamma_0(4)$.