  We prove a $k^{-\Omega(\log(\varepsilon_2 - \varepsilon_1))}$ lower bound for
adaptively testing whether a Boolean function is $\varepsilon_1$-close to or
$\varepsilon_2$-far from $k$-juntas. Our results provide the first
superpolynomial separation between tolerant and non-tolerant testing for a
natural property of boolean functions under the adaptive setting. Furthermore,
our techniques generalize to show that adaptively testing whether a function is
$\varepsilon_1$-close to a $k$-junta or $\varepsilon_2$-far from $(k +
o(k))$-juntas cannot be done with $\textsf{poly} (k, (\varepsilon_2 -
\varepsilon_1)^{-1})$ queries. This is in contrast to an algorithm by Iyer, Tal
and Whitmeyer [CCC 2021] which uses $\textsf{poly} (k, (\varepsilon_2 -
\varepsilon_1)^{-1})$ queries to test whether a function is
$\varepsilon_1$-close to a $k$-junta or $\varepsilon_2$-far from
$O(k/(\varepsilon_2-\varepsilon_1)^2)$-juntas.
