Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity
Abstract We investigate the formulation of Vasiliev’s four-dimensional higher-spin gravity in operator form, without making reference to one specific ordering. More precisely, we make use of the one-to-one mapping between operators and symbols thereof for a family of ordering prescriptions that inte...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2022)003 |
| _version_ | 1818488286591582208 |
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| author | David De Filippi Carlo Iazeolla Per Sundell |
| author_facet | David De Filippi Carlo Iazeolla Per Sundell |
| author_sort | David De Filippi |
| collection | DOAJ |
| description | Abstract We investigate the formulation of Vasiliev’s four-dimensional higher-spin gravity in operator form, without making reference to one specific ordering. More precisely, we make use of the one-to-one mapping between operators and symbols thereof for a family of ordering prescriptions that interpolate between and go beyond Weyl and normal orderings. This correspondence allows us to perturbatively integrate the Vasiliev system in operator form and in a variety of gauges. Expanding the master fields in inhomogenous symplectic group elements, and letting products be controlled only by the group, we specify a family of factorized gauges in which we are able to integrate the system to all orders, producing exact solutions, including but not restricted to ones presented previously in the literature; and then connect, at first order, to a family of rotated Vasiliev gauges in which the solutions can be represented in terms of Fronsdal fields. The gauge function responsible for the latter transformation is explicitly constructed at first order. The analysis of the system in various orderings is facilitated by an analytic continuation of Gaussian symbols, by means of which one can distinguish and connect the two branches of the metaplectic double cover and give a rationale to the properties of the inner Klein operators as Gaussian delta sequences defining analytic delta densities. As an application of some of the techniques here developed, we evaluate twistor space Wilson line observables on our exact solutions and show their independence from auxiliary constructs up to the few first subleading orders in perturbation theory. |
| first_indexed | 2024-12-10T16:48:59Z |
| format | Article |
| id | doaj.art-26b48a0b302e49b29e6244e1345e298f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T16:48:59Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-26b48a0b302e49b29e6244e1345e298f2022-12-22T01:40:56ZengSpringerOpenJournal of High Energy Physics1029-84792022-07-0120227110610.1007/JHEP07(2022)003Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravityDavid De Filippi0Carlo Iazeolla1Per Sundell2Physics of the Universe, Fields and Gravitation University of Mons — UMONSDipartimento di Scienze Ingegneristiche, Guglielmo Marconi UniversityCentro de Ciencias Exactas, Universidad del Bío-BíoAbstract We investigate the formulation of Vasiliev’s four-dimensional higher-spin gravity in operator form, without making reference to one specific ordering. More precisely, we make use of the one-to-one mapping between operators and symbols thereof for a family of ordering prescriptions that interpolate between and go beyond Weyl and normal orderings. This correspondence allows us to perturbatively integrate the Vasiliev system in operator form and in a variety of gauges. Expanding the master fields in inhomogenous symplectic group elements, and letting products be controlled only by the group, we specify a family of factorized gauges in which we are able to integrate the system to all orders, producing exact solutions, including but not restricted to ones presented previously in the literature; and then connect, at first order, to a family of rotated Vasiliev gauges in which the solutions can be represented in terms of Fronsdal fields. The gauge function responsible for the latter transformation is explicitly constructed at first order. The analysis of the system in various orderings is facilitated by an analytic continuation of Gaussian symbols, by means of which one can distinguish and connect the two branches of the metaplectic double cover and give a rationale to the properties of the inner Klein operators as Gaussian delta sequences defining analytic delta densities. As an application of some of the techniques here developed, we evaluate twistor space Wilson line observables on our exact solutions and show their independence from auxiliary constructs up to the few first subleading orders in perturbation theory.https://doi.org/10.1007/JHEP07(2022)003Higher Spin GravityHigher Spin Symmetry |
| spellingShingle | David De Filippi Carlo Iazeolla Per Sundell Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity Journal of High Energy Physics Higher Spin Gravity Higher Spin Symmetry |
| title | Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity |
| title_full | Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity |
| title_fullStr | Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity |
| title_full_unstemmed | Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity |
| title_short | Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity |
| title_sort | metaplectic representation and ordering in dependence in vasiliev s higher spin gravity |
| topic | Higher Spin Gravity Higher Spin Symmetry |
| url | https://doi.org/10.1007/JHEP07(2022)003 |
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