  We propose a novel jet substructure observable of boosted tops that is
related to the linear polarization of the $W$ boson in boosted top quark decay,
which results in a $\cos2\phi$ angular correlation between the $t\to bW$ and
$W\to f\bar{f'}$ decay planes. We discuss in detail the origin of such linear
polarization by applying Wigner's little group transformation. We show that the
unique $\cos2\phi$ angular correlation only exists in the boosted regime but
not in the top quark rest frame. We construct an experimental observable for
such correlation based on the transverse energy deposition asymmetry in the top
jet that does not require the reconstruction of $W$ decay products. The degree
of this asymmetry can be used to measure the longitudinal polarization of the
top quark, which is an important probe of new physics that couples to the top
sector, and can discriminate a boosted top quark jet from its background
events, such as QCD jets. A numerical simulation is also performed and found to
agree well with the analytic prediction of the Standard Model.
