Twisting and localization in supergravity: equivariant cohomology of BPS black holes

Imtak Jeon (Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211019, India) ; Sameer Murthy (Department of Mathematics, King’s College London, The Strand, London, WC2R 2LS, U.K.)

We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in [1]. The gravitational functional integral localizes onto the cohomology of a global supercharge Q eq, obeying Q eq 2 = H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N $$ \mathcal{N} $$ = 2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the Q eq V $$ \mathcal{V} $$ deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2 × S 2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.

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  "abstracts": [
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      "source": "Springer", 
      "value": "We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in [1]. The gravitational functional integral localizes onto the cohomology of a global supercharge Q eq, obeying Q  eq 2  = H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the Q eq   <math> <mi>V</mi> </math>  $$ \\mathcal{V} $$  deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2 \u00d7 S 2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy."
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Published on:
25 March 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 3
Pages 1-53
DOI:
https://doi.org/10.1007/JHEP03(2019)140
arXiv:
1806.04479
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

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