Conformal blocks in two and four dimensions from oscillator representations
Abstract The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We demonstrate this by reproducing the general n-point global...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)091 |
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| _version_ | 1849725502868160512 |
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| author | Martin Ammon Jakob Hollweck Tobias Hössel Katharina Wölfl |
| author_facet | Martin Ammon Jakob Hollweck Tobias Hössel Katharina Wölfl |
| author_sort | Martin Ammon |
| collection | DOAJ |
| description | Abstract The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We demonstrate this by reproducing the general n-point global conformal block in the comb channel in an elegant and direct manner. Exploiting similarities to the representation theory of two-dimensional CFTs, we extend the oscillator formalism to the computation of higher-point conformal blocks in four Euclidean dimensions. As a proof of concept, we explicitly compute the scalar four-point block with scalar exchange within this framework and discuss the extension to the higher-point case. |
| format | Article |
| id | doaj-art-d370b0ffd0d044d78a81e1819b4eb691 |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d370b0ffd0d044d78a81e1819b4eb6912025-08-20T03:10:27ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025513410.1007/JHEP05(2025)091Conformal blocks in two and four dimensions from oscillator representationsMartin Ammon0Jakob Hollweck1Tobias Hössel2Katharina Wölfl3Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität JenaTheoretisch-Physikalisches Institut, Friedrich-Schiller-Universität JenaTheoretisch-Physikalisches Institut, Friedrich-Schiller-Universität JenaTheoretisch-Physikalisches Institut, Friedrich-Schiller-Universität JenaAbstract The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We demonstrate this by reproducing the general n-point global conformal block in the comb channel in an elegant and direct manner. Exploiting similarities to the representation theory of two-dimensional CFTs, we extend the oscillator formalism to the computation of higher-point conformal blocks in four Euclidean dimensions. As a proof of concept, we explicitly compute the scalar four-point block with scalar exchange within this framework and discuss the extension to the higher-point case.https://doi.org/10.1007/JHEP05(2025)091Scale and Conformal SymmetriesField Theories in Higher DimensionsField Theories in Lower Dimensions |
| spellingShingle | Martin Ammon Jakob Hollweck Tobias Hössel Katharina Wölfl Conformal blocks in two and four dimensions from oscillator representations Journal of High Energy Physics Scale and Conformal Symmetries Field Theories in Higher Dimensions Field Theories in Lower Dimensions |
| title | Conformal blocks in two and four dimensions from oscillator representations |
| title_full | Conformal blocks in two and four dimensions from oscillator representations |
| title_fullStr | Conformal blocks in two and four dimensions from oscillator representations |
| title_full_unstemmed | Conformal blocks in two and four dimensions from oscillator representations |
| title_short | Conformal blocks in two and four dimensions from oscillator representations |
| title_sort | conformal blocks in two and four dimensions from oscillator representations |
| topic | Scale and Conformal Symmetries Field Theories in Higher Dimensions Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP05(2025)091 |
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