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 $$ \mathcal{N} $$ = 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 $$ \mathcal{V} $$ 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.
{ "_oai": { "updated": "2019-03-27T09:30:48Z", "id": "oai:repo.scoap3.org:46400", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "India", "value": "Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211019, India", "organization": "Harish-Chandra Research Institute" } ], "surname": "Jeon", "email": "imtakjeon@gmail.com", "full_name": "Jeon, Imtak", "given_names": "Imtak" }, { "affiliations": [ { "country": "UK", "value": "Department of Mathematics, King\u2019s College London, The Strand, London, WC2R 2LS, U.K.", "organization": "King\u2019s College London" } ], "surname": "Murthy", "email": "sameer.murthy@kcl.ac.uk", "full_name": "Murthy, Sameer", "given_names": "Sameer" } ], "titles": [ { "source": "Springer", "title": "Twisting and localization in supergravity: equivariant cohomology of BPS black holes" } ], "dois": [ { "value": "10.1007/JHEP03(2019)140" } ], "publication_info": [ { "page_end": "53", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2019", "artid": "JHEP032019140", "year": 2019, "page_start": "1", "journal_issue": "3" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2019-03-27T10:30:28.799028", "source": "Springer", "method": "Springer", "submission_number": "e8283994507211e9a1e502163e01809a" }, "page_nr": [ 53 ], "license": [ { "url": "https://creativecommons.org/licenses/by/3.0", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2019" } ], "control_number": "46400", "record_creation_date": "2019-03-27T10:30:28.799055", "_files": [ { "checksum": "md5:9390b80d1f28666fc375b263554d5a68", "filetype": "xml", "bucket": "47f4002b-55d1-4689-bb14-f69d882e791c", "version_id": "a5aa05f4-a0e6-48b5-a1ae-b54e6a71270c", "key": "10.1007/JHEP03(2019)140.xml", "size": 11740 }, { "checksum": "md5:128226e93a70f16143e0971a40ce3bd3", "filetype": "pdf/a", "bucket": "47f4002b-55d1-4689-bb14-f69d882e791c", "version_id": "eb68ede7-169c-4b4c-b5cc-b2ef67d47e32", "key": "10.1007/JHEP03(2019)140_a.pdf", "size": 843278 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th" ], "value": "1806.04479" } ], "abstracts": [ { "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." } ], "imprints": [ { "date": "2019-03-25", "publisher": "Springer" } ] }