  In light of recent developments demonstrating the impact of cavity vacuum
fields inducing the breakdown of topological protection in the integer quantum
Hall effect, a compelling question arises: what effects might cavity vacuum
fields have on fundamental constants in solid-state systems? In this work we
present an experiment that assesses the possibility of the von Klitzing
constant itself being modified. By employing a Wheatstone bridge, we precisely
measure the difference between the quantized Hall resistance of a
cavity-embedded Hall bar and the resistance standard, achieving an accuracy
down to 1 part in 105 for the lowest Landau level. While our results do not
suggest any deviation that could imply a modified Hall resistance, our work
represents pioneering efforts in exploring the fundamental implications of
vacuum fields in solid-state systems.
