  We show that perturbations of massless fields in the Kerr black hole
background enjoy a hidden $SL(2,\mathbb{R})\times {U}(1)$ ("Love") symmetry in
the properly defined near zone approximation. Love symmetry mixes IR and UV
modes. Still, this approximate symmetry allows us to derive exact results about
static tidal responses. Generators of the Love symmetry are globally well
defined and have a smooth Schwarzschild limit. Generic regular solutions of the
near zone Teukolsky equation form infinite-dimensional $SL(2,\mathbb{R})$
representations. In some special cases ($\hat{\ell}$ parameter is an integer),
these are highest weight representations. This is the situation that
corresponds to vanishing Love numbers. In particular, static perturbations of
four-dimensional Schwarzschild black holes belong to finite-dimensional
representations. Other known facts about static Love numbers also acquire an
elegant explanation in terms of the $SL(2,\mathbb{R})$ representation theory.
