Entanglement entropy of gravitational edge modes
Abstract We consider the linearised graviton in 4d Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere labels the superselection sectors for the gravito...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2022)065 |
| _version_ | 1798037955063840768 |
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| author | Justin R. David Jyotirmoy Mukherjee |
| author_facet | Justin R. David Jyotirmoy Mukherjee |
| author_sort | Justin R. David |
| collection | DOAJ |
| description | Abstract We consider the linearised graviton in 4d Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere labels the superselection sectors for the graviton. We show that among these 6 normal components of the Riemann tensor, 2 are related locally to the algebra of gauge-invariant operators in the sphere. From the two-point function of these components of the Riemann tensor on S 2 we compute the logarithmic coefficient of the entanglement entropy of these superselection sectors across a spherical entangling surface. For sectors labelled by each of the two components of the Riemann tensor these coefficients are equal and their total contribution is given by − 16 3 $$ -\frac{16}{3} $$ . We observe that this coefficient coincides with that extracted from the edge partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character. As a preliminary step, we also evaluate the logarithmic coefficient of the entanglement entropy from the superselection sectors labelled by the radial component of the electric field of the U(1) theory in even d dimensions. We show that this agrees with the corresponding coefficient of the edge Harish-Chandra character of the massless spin-1 field on S d . |
| first_indexed | 2024-04-11T21:33:37Z |
| format | Article |
| id | doaj.art-095253c401094d1d9a78d34d205174c2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T21:33:37Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-095253c401094d1d9a78d34d205174c22022-12-22T04:01:50ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022813910.1007/JHEP08(2022)065Entanglement entropy of gravitational edge modesJustin R. David0Jyotirmoy Mukherjee1Centre for High Energy Physics, Indian Institute of ScienceCentre for High Energy Physics, Indian Institute of ScienceAbstract We consider the linearised graviton in 4d Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere labels the superselection sectors for the graviton. We show that among these 6 normal components of the Riemann tensor, 2 are related locally to the algebra of gauge-invariant operators in the sphere. From the two-point function of these components of the Riemann tensor on S 2 we compute the logarithmic coefficient of the entanglement entropy of these superselection sectors across a spherical entangling surface. For sectors labelled by each of the two components of the Riemann tensor these coefficients are equal and their total contribution is given by − 16 3 $$ -\frac{16}{3} $$ . We observe that this coefficient coincides with that extracted from the edge partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character. As a preliminary step, we also evaluate the logarithmic coefficient of the entanglement entropy from the superselection sectors labelled by the radial component of the electric field of the U(1) theory in even d dimensions. We show that this agrees with the corresponding coefficient of the edge Harish-Chandra character of the massless spin-1 field on S d .https://doi.org/10.1007/JHEP08(2022)065Gauge SymmetryScale and Conformal Symmetries |
| spellingShingle | Justin R. David Jyotirmoy Mukherjee Entanglement entropy of gravitational edge modes Journal of High Energy Physics Gauge Symmetry Scale and Conformal Symmetries |
| title | Entanglement entropy of gravitational edge modes |
| title_full | Entanglement entropy of gravitational edge modes |
| title_fullStr | Entanglement entropy of gravitational edge modes |
| title_full_unstemmed | Entanglement entropy of gravitational edge modes |
| title_short | Entanglement entropy of gravitational edge modes |
| title_sort | entanglement entropy of gravitational edge modes |
| topic | Gauge Symmetry Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP08(2022)065 |
| work_keys_str_mv | AT justinrdavid entanglemententropyofgravitationaledgemodes AT jyotirmoymukherjee entanglemententropyofgravitationaledgemodes |