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.
3d defects in 5d: RG flows and defect F-maximization
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We use a combination of AdS/CFT and supersymmetric localization to study codimension-2 defects in 5d SCFTs and their gauge theory deformations. The 5d SCFTs are engineered by $(p,q)$ 5-brane webs, with defects realized by D3-branes ending on the 5-brane webs. We obtain the defect free energies and find that gauge theory descriptions of the combined 5d/3d systems can be connected to the UV defect SCFTs through a form of F-maximization which extremizes over different gauge theory defects. This leads to a match between the defect free energies obtained from supersymmetric localization in the gauge theories on the one hand and string theory results on the other. We extend this match to defect RG flows.
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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.