All rotation-invariant superconformal defects satisfy CD/aT = -2(n-1)(p+2)Γ(p+1)/(n π^{p-n/2} Γ(p/2+1)Γ((n-p)/2)), proved from supersymmetric Ward identities.
General Definition of Gravitational Tension
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In this note we give a general definition of the gravitational tension in a given asymptotically translationally-invariant spatial direction of a space-time. The tension is defined via the extrinsic curvature in analogy with the Hawking-Horowitz definition of energy. We show the consistency with the ADM tension formulas for asymptotically-flat space-times, in particular for Kaluza-Klein black hole solutions. Moreover, we apply the general tension formula to near-extremal branes, constituting a check for non-asymptotically flat space-times.
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An unusual BPS equation
All rotation-invariant superconformal defects satisfy CD/aT = -2(n-1)(p+2)Γ(p+1)/(n π^{p-n/2} Γ(p/2+1)Γ((n-p)/2)), proved from supersymmetric Ward identities.