Projectors and seed conformal blocks for traceless mixed-symmetry tensors

In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of...

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Autores principales: Costa, Miguel S., Hansen, Tobias, Penedones, João, Trevisani, Emilio
Lenguaje:eng
Publicado: 2016
Materias:
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1007/JHEP07(2016)018
http://cds.cern.ch/record/2140220
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author Costa, Miguel S.
Hansen, Tobias
Penedones, João
Trevisani, Emilio
author_facet Costa, Miguel S.
Hansen, Tobias
Penedones, João
Trevisani, Emilio
author_sort Costa, Miguel S.
collection CERN
description In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2016
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spelling cern-21402202023-10-04T06:39:14Zdoi:10.1007/JHEP07(2016)018http://cds.cern.ch/record/2140220engCosta, Miguel S.Hansen, TobiasPenedones, JoãoTrevisani, EmilioProjectors and seed conformal blocks for traceless mixed-symmetry tensorsParticle Physics - TheoryIn this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length l$_{1}$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in l$_{1}$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.arXiv:1603.05551CERN-TH-2016-080CERN-TH-2016-080oai:cds.cern.ch:21402202016-03-17
spellingShingle Particle Physics - Theory
Costa, Miguel S.
Hansen, Tobias
Penedones, João
Trevisani, Emilio
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
title Projectors and seed conformal blocks for traceless mixed-symmetry tensors
title_full Projectors and seed conformal blocks for traceless mixed-symmetry tensors
title_fullStr Projectors and seed conformal blocks for traceless mixed-symmetry tensors
title_full_unstemmed Projectors and seed conformal blocks for traceless mixed-symmetry tensors
title_short Projectors and seed conformal blocks for traceless mixed-symmetry tensors
title_sort projectors and seed conformal blocks for traceless mixed-symmetry tensors
topic Particle Physics - Theory
url https://dx.doi.org/10.1007/JHEP07(2016)018
http://cds.cern.ch/record/2140220
work_keys_str_mv AT costamiguels projectorsandseedconformalblocksfortracelessmixedsymmetrytensors
AT hansentobias projectorsandseedconformalblocksfortracelessmixedsymmetrytensors
AT penedonesjoao projectorsandseedconformalblocksfortracelessmixedsymmetrytensors
AT trevisaniemilio projectorsandseedconformalblocksfortracelessmixedsymmetrytensors

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