Faking gauge coupling unification in string theory

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 4D 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\"ahler moduli space. We prove that a strong calibration is preserved under appropriate topological transitions and that a pair of nonintersecting divisors each admitting a contraction can always be strongly calibrated. Within the tree ensemble [J. Halverson et al., Phys. Rev. D 96, 126006 (2017)], we find that $\ensuremath{\approx}77.12%$ of pairs of intersecting toric divisors can be strongly calibrated and $\ensuremath{\approx}3.22%$ can never be calibrated. Physically, this means that gauge coupling unification can be faked in most cases that we study, but in others it can not, which is surprising from a gauge theoretic perspective.