  Advances in high-precision dielectric spectroscopy has enabled access to
non-linear susceptibilities of polar molecular liquids. The observed
non-monotonic behavior has been claimed to provide strong support for theories
of dynamic arrest based on thermodynamic amorphous order. Here we approach this
question from the perspective of dynamic facilitation, an alternative view
focusing on emergent kinetic constraints underlying the dynamic arrest of a
liquid approaching its glass transition. We derive explicit expressions for the
frequency-dependent higher-order dielectric susceptibilities exhibiting a
non-monotonic shape, the height of which increases as temperature is lowered.
We demonstrate excellent agreement with the experimental data for glycerol,
challenging the idea that non-linear response functions reveal correlated
relaxation in supercooled liquids.
