Faking Gauge Coupling Unification in String Theory

TL;DR

This paper investigates how gauge coupling unification can be mimicked in string theory F-theory compactifications through a concept called strong calibration, revealing that such faking is possible in most cases but not all.

Contribution

It introduces the strong calibration condition for gauge couplings in F-theory and analyzes its preservation and prevalence within the Tree ensemble, highlighting its implications for unification.

Findings

Approximately 77.12% of intersecting divisor pairs can be strongly calibrated.

About 3.22% of divisor pairs can never be calibrated.

Gauge coupling unification can often be faked in string theory, challenging gauge theoretic expectations.

Abstract

Gauge coupling unification misleads infrared observers if new gauge bosons do not simultaneously come into the spectrum. Though easy to engineer in gauge theory, the situation in string theory is nuanced, due to moduli dependence. We study the possibility of faking gauge coupling unification in the context of $4$d F-theory compactifications. Specifically, we formulate a sufficient condition that we call a strong calibration, under which seven-brane gauge couplings on homologically distinct divisors become equal at codimension one in K\"{a}hler moduli space. We prove that a strong calibration is preserved under appropriate topological transitions and that a pair of non-intersecting divisors each admitting a contraction can always be strongly calibrated. Within the Tree ensemble, we find that $\approx 77.12\%$ of pairs of intersecting toric divisors can be strongly calibrated and $\approx 3.22\%$ can never be calibrated. Physically, this means that gauge coupling unification can be faked in most cases that we study, but in others it cannot, which is surprising from a gauge theoretic perspective.