Affine Algebras at Infinite Distance Limits in the Heterotic String

TL;DR

This paper investigates the behavior of affine algebras at infinite distance limits in heterotic string compactifications, revealing new algebraic structures and towers of states that emerge in dual frames, especially in $T^2$ compactifications.

Contribution

It provides a detailed analysis of the affine algebra structures at infinite distance limits in heterotic string theory and their F-theory duals, including explicit constructions of new affine algebras.

Findings

Reproduces all affine algebras in $T^2$ compactifications and their towers.

Constructs the affine $SO(32)$ algebra in full decompactification limits.

Shows that non-exceptional affine algebras also arise in F-theory duals.

Abstract

We analyze the boundaries of the moduli spaces of compactifications of the heterotic string on $T^d$, making particular emphasis on $d=2$ and its F-theory dual. We compute the OPE algebras as we approach all the infinite distance limits that correspond to (possibly partial) decompactification limits in some dual frame. When decompactifying $k$ directions, we find infinite towers of states becoming light that enhance the algebra arising at a given point in the moduli space of the $T^{d-k}$ compactification to its $k$-loop version, where the central extensions are given by the $k$ KK vectors. For $T^2$ compactifications, we reproduce all the affine algebras that arise in the F-theory dual, and show all the towers explicitly, including some that are not manifest in the F-theory counterparts. Furthermore, we construct the affine $SO(32)$ algebra arising in the full decompactification limit, both in the heterotic and in the F-theory sides, showing that not only affine algebras of exceptional type arise in the latter.