Monodromy methods for torus conformal blocks and entanglement entropy at large central charge
Abstract We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Th...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2021)143 |
| _version_ | 1818358225198645248 |
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| author | Marius Gerbershagen |
| author_facet | Marius Gerbershagen |
| author_sort | Marius Gerbershagen |
| collection | DOAJ |
| description | Abstract We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Then, we derive a monodromy method for the zero-point conformal blocks of the replica partition function. We explain the differences between the two monodromy methods before applying them to the calculation of the entanglement entropy. We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula. Moreover, we determine in which regime the replica partition function agrees with a correlation function of local twist operators on the torus. |
| first_indexed | 2024-12-13T20:25:37Z |
| format | Article |
| id | doaj.art-cc6854f3b2404b22bdecc6000ce03ea8 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T20:25:37Z |
| publishDate | 2021-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-cc6854f3b2404b22bdecc6000ce03ea82022-12-21T23:32:34ZengSpringerOpenJournal of High Energy Physics1029-84792021-08-012021813210.1007/JHEP08(2021)143Monodromy methods for torus conformal blocks and entanglement entropy at large central chargeMarius Gerbershagen0Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität WürzburgAbstract We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Then, we derive a monodromy method for the zero-point conformal blocks of the replica partition function. We explain the differences between the two monodromy methods before applying them to the calculation of the entanglement entropy. We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula. Moreover, we determine in which regime the replica partition function agrees with a correlation function of local twist operators on the torus.https://doi.org/10.1007/JHEP08(2021)143Conformal Field TheoryAdS-CFT Correspondence |
| spellingShingle | Marius Gerbershagen Monodromy methods for torus conformal blocks and entanglement entropy at large central charge Journal of High Energy Physics Conformal Field Theory AdS-CFT Correspondence |
| title | Monodromy methods for torus conformal blocks and entanglement entropy at large central charge |
| title_full | Monodromy methods for torus conformal blocks and entanglement entropy at large central charge |
| title_fullStr | Monodromy methods for torus conformal blocks and entanglement entropy at large central charge |
| title_full_unstemmed | Monodromy methods for torus conformal blocks and entanglement entropy at large central charge |
| title_short | Monodromy methods for torus conformal blocks and entanglement entropy at large central charge |
| title_sort | monodromy methods for torus conformal blocks and entanglement entropy at large central charge |
| topic | Conformal Field Theory AdS-CFT Correspondence |
| url | https://doi.org/10.1007/JHEP08(2021)143 |
| work_keys_str_mv | AT mariusgerbershagen monodromymethodsfortorusconformalblocksandentanglemententropyatlargecentralcharge |