Boundary conditions and localization on AdS: Part 2 General analysis

Understand

We develop the method of Green's function to evaluate the one loop determinants that arise in localization of supersymmetric field theories on $AdS$ spaces.

• The theories we study have at least ${\cal N}=2$ supersymmetry and normalisable boundary conditions are consistent with supersymmetry.
• We then show that under general assumptions the variation of the one loop determinant with respect to the localizing background reduces to a total derivative.
• Therefore it receives contributions only from the origin of $AdS$ and from asymptotic infinity.