Large-Volume String Compactifications, Revisited

TL;DR

This paper revisits large-volume heterotic string compactifications, concluding that a fundamental limit on the Kaluza-Klein scale exists due to an additional low-energy threshold, challenging classical compactification assumptions.

Contribution

It introduces a new reason for the limitations on large-volume heterotic compactifications, emphasizing the role of an additional threshold at low energies.

Findings

Kaluza-Klein scale must be greater than 4×10^7 GeV.

The actual limit is often much higher.

Kaluza-Klein scale exceeds alpha_GUT times Planck mass in typical models.

Abstract

We reconsider the issue of large-volume compactifications of the heterotic string in light of the recent discoveries about strongly-coupled string theories. Our conclusion remains firmly negative with respect to classical compactifications of the ten-dimensional field theory, albeit for a new reason: When the internal sixfold becomes large in heterotic units, the theory acquires an additional threshold at energies much less then the naive Kaluza-Klein scale. It is this additional threshold that imposes the ultimate limit on the compactification scale: Any compactification must have M_{Kaluza Klein} > 4*10^7 Gev; for most compactifications, the actual limit is much higher. (Generically, M_{Kaluza Klein} > alpha_{GUT} M_{Planck} in either SO(32) or E_8*E_8 heterotic string.)