  We revisit the problem of defining an invariant notion of tension in gravity.
For spacetimes whose asymptotics are those of a Defect CFT we propose two
independent definitions : Gravitational tension given by the one-point function
of the dilatation current, and inertial tension, or stiffness, given by the
norm of the displacement operator. We show that both reduce to the tension of
the Nambu-Goto action in the limit of classical thin probe branes. Subtle
normalisations of the relevant Witten diagrams are fixed by the Weyl and
diffeomorphism Ward identities of the boundary DCFT. The gravitational tension
is not defined for domain walls, whereas stiffness is not defined for point
particles. When they both exist these two tensions are in general different,
but the examples of line and surface BPS defects in $d=4$ show that
superconformal invariance can identify them.
