Mass hierarchies and dynamical field range

Several swampland conjectures suggest that there is a critical field range beyond which the effective field theory (EFT) description breaks down in quantum gravity. In applications of these conjectures, however, the field range of interest is the field space distance traced by the physical trajectory that solves the equations of motion. We refer to this field space distance as the dynamical field range. We show that in the absence of a mass hierarchy between the light and heavy fields, the trajectory of the light field does not, in general, follow a geodesic in field space. Then, stabilizing the heavy fields at the minimum of their potential does not accurately describe the dynamics of the light field in general. A mass hierarchy can delay the breakdown of the EFT and extend the effective field range. We illustrate these subtleties of multifield dynamics with axions in type II string compactifications.

Figure 1

Field ranges obtained by (7) (blue) and (4) (orange) for $\frac{{\mathfrak{f}}_0}{\mu }\sim {10}^4$ and $G_{\phi \overline{\phi }}{|}_0\sim 2\times {10}^{-1}$.

Figure 2

Field range obtained by (7) (blue) and (4) (orange) for $\frac{{\mathfrak{f}}_0}{\mu }\sim 1$ and $G_{\phi \overline{\phi }}{|}_0\sim 2\times {10}^{-1}$. In this case ${\widehat{\phi }}_{\mathrm{app}}\sim 0.1M_{\mathrm{Pl}}$ for $ϵ=0.1$.