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.

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      "title": "Localization on AdS3 \u00d7 S2. Part I. The 4d/5d connection in off-shell Euclidean supergravity"
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      "source": "Springer", 
      "value": "We begin to develop the formalism of localization for the functional integral of supergravity on AdS3 \u00d7 S2. We show how the condition of supersymmetry in the Euclidean \u210d3 /\u2124 \u00d7 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 \u210d3 /\u2124 \u00d7 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 \u00d7 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."
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Published on:
28 July 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 7
Pages 1-45
DOI:
https://doi.org/10.1007/JHEP07(2023)218
arXiv:
2301.08084
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: