Invariant tensions from holography

TL;DR

This paper explores invariant definitions of tension in gravity for defect conformal field theories, proposing two approaches and analyzing their relations and special cases.

Contribution

It introduces two independent definitions of tension—gravitational and inertial—in the context of defect CFTs and clarifies their relation in supersymmetric cases.

Findings

Both tensions reduce to Nambu-Goto tension for classical probe branes.

Normalizations are fixed by Ward identities of the boundary DCFT.

Superconformal invariance can unify the two tensions in certain BPS defect cases.

Abstract

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.