Giant transverse magnetic fluctuations at the edge of re-entrant superconductivity in UTe$_{2}$

UTe$_{2}$ exhibits the remarkable phenomenon of re-entrant superconductivity, whereby the zero-resistance state reappears above 40 tesla after being suppressed with a field of around 10 tesla. One potential pairing mechanism, invoked in the related re-entrant superconductors UCoGe and URhGe, involves transverse fluctuations of a ferromagnetic order parameter. However, the requisite ferromagnetic order - present in both UCoGe and URhGe - is absent in UTe$_{2}$, and magnetization measurements show no sign of strong fluctuations. Here, we measure the magnetotropic susceptibility of UTe$_{2}$ across two field-angle planes. This quantity is sensitive to the magnetic susceptibility in a direction transverse to the applied magnetic field - a quantity that is not accessed in conventional magnetization measurements. We observe a very large decrease in the magnetotropic susceptibility over a broad range of field orientations, indicating a large increase in the transverse magnetic susceptibility. The three superconducting phases of UTe$_{2}$, including the high-field re-entrant phase, surround this region of enhanced susceptibility in the field-angle phase diagram. The strongest transverse susceptibility is found near the critical end point of the high-field metamagnetic transition, suggesting that quantum critical fluctuations of a field-induced magnetic order parameter may be responsible for the large transverse susceptibility, and may provide a pairing mechanism for field-induced superconductivity in UTe$_{2}$.