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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Main Authors: Martin Ammon, Jakob Hollweck, Tobias Hössel, Katharina Wölfl
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP05(2025)091
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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
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institution DOAJ
issn 1029-8479
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publishDate 2025-05-01
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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
work_keys_str_mv AT martinammon conformalblocksintwoandfourdimensionsfromoscillatorrepresentations
AT jakobhollweck conformalblocksintwoandfourdimensionsfromoscillatorrepresentations
AT tobiashossel conformalblocksintwoandfourdimensionsfromoscillatorrepresentations
AT katharinawolfl conformalblocksintwoandfourdimensionsfromoscillatorrepresentations