Localization on AdS3 × S2. Part I. The 4d/5d connection in off-shell Euclidean supergravity
Axel Ciceri (Department of Mathematics, King’s College London, The Strand, London, WC2R 2LS, UK); Imtak Jeon (Asia Pacific Center for Theoretical Physics, Postech, Pohang, 37673, Korea, Department of Physics, Postech, Pohang, 37673, Korea); Sameer Murthy (Department of Mathematics, King’s College London, The Strand, London, WC2R 2LS, UK)
We begin to develop the formalism of localization for the functional integral of supergravity on AdS3 × S2. We show how the condition of supersymmetry in the Euclidean ℍ3 /ℤ × S2 geometry naturally leads to a twist of the S2 around the time direction of AdS3. The twist gives us a five-dimensional Euclidean supergravity background dual to the elliptic genus of (0, 4) SCFT2 at the semiclassical level. On this background we set up the off-shell BPS equations for one of the Killing spinors, such that the functional integral of five-dimensional Euclidean supergravity on ℍ3 /ℤ × S2 localizes to its space of solutions. We obtain a class of solutions to these equations by lifting known off-shell BPS solutions of 4-dimensional supergravity on AdS2 × S2. In order to do this consistently, we construct and use a Euclidean version of the off-shell 4d/5d lift of arXiv:1112.5371 , which could be of independent interest.
