  There has been proposed two continuum descriptions of fracton systems:
foliated quantum field theories (FQFTs) and exotic quantum field theories.
Certain fracton systems are believed to admit descriptions by both, and hence a
duality is expected between such a class of FQFTs and exotic QFTs. In this
paper we study this duality in detail for concrete examples in $2+1$ and $3+1$
dimensions. In the examples, both sides of the continuum theories are of
$BF$-type, and we find the explicit correspondences of gauge-invariant
operators, gauge fields, parameters, and allowed singularities and
discontinuities. This deepens the understanding of dualities in fractonic
quantum field theories.
