English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We evaluate the low energy gravitational couplings, $F_g$ in the heterotic$E_8\times E_8$ string theory compactified on orbifolds of $K3\times T^2$ by$g'$ which acts as a $\mathbb{Z}_N$ automorphisim on $K3$ together with a $1/N$shift along $T^2$. The orbifold $g'$ corresponds to the conjugacy classes ofthe Mathieu group $M_{24}$. The holomorphic piece of $F_g$ is given in terms ofa polylogarithim with index $3-2g$ and predicts the Gopakumar-Vafa invariantsin the corresponding dual type II Calabi-Yau compactifications. We show thatlow lying Gopakumar-Vafa invariants for each of these compactificationsincluding the twisted sectors are integers. We observe that the conifoldsingularity for all these compactifications occurs only when states in thetwisted sectors become massless and the strength of the singularity isdetermined by the genus zero Gopakumar-Vafa invariant at this point in themoduli space.

Gravitational couplings in ${\cal N}=2$ string compactifications and Mathieu Moonshine