  The Klebanov-Tarnopolsky tensor model is a quantum field theory for
rank-three tensor scalar fields with certain quartic potential. The theory
possesses an unusual large $N$ limit known as the melonic limit that is
strongly coupled yet solvable, producing at large distance a rare example of
non-perturbative non-supersymmetric conformal field theory that admits analytic
solutions. We study the dynamics of defects in the tensor model defined by
localized magnetic field couplings on a $p$-dimensional subspace in the
$d$-dimensional spacetime. While we work with general $p$ and $d$, the
physically interesting cases include line defects in $d=2,3$ and surface
defects in $d=3$. By identifying a novel large $N$ limit that generalizes the
melonic limit in the presence of defects, we prove that the defect one-point
function of the scalar field only receives contributions from a subset of the
Feynman diagrams in the shape of melonic trees. These diagrams can be resummed
using a closed Schwinger-Dyson equation which enables us to determine
non-perturbatively this defect one-point function. At large distance, the
solutions we find describe nontrivial conformal defects and we discuss their
defect renormalization group (RG) flows. In particular, for line defects, we
solve the exact RG flow between the trivial and the conformal lines in
$d=4-\epsilon$. We also compute the exact line defect entropy and verify the
$g$-theorem. Furthermore we analyze the defect two-point function of the scalar
field and its decomposition via the operator-product-expansion, providing
explicit formulae for one-point functions of bilinear operators and the
stress-energy tensor.
