Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913979099512832 |
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| author | Ammon, Martin Hollweck, Jakob Hössel, Tobias Wölfl, Katharina |
| author_facet | Ammon, Martin Hollweck, Jakob Hössel, Tobias Wölfl, Katharina |
| contents | We define and compute the four-dimensional thermal $n$-point conformal block in the projection channel using oscillator representations on $\mathbb{S}^1_β\times \mathbb{S}^3$. This is done by evaluating a class of integrals over the homogeneous space $\mathbb{D}_4$ of the four-dimensional conformal group. We restrict ourselves to scalar external operators and scalar exchange. In the low-temperature limit, our result reduces correctly to the vacuum $(n+2)$-point block in the comb channel. The corresponding expressions can be written as a series of terminating hypergeometric functions or equivalently, a series of weighted SU(2) spin-networks. Alternatively, functions adapted to the SU(2,2) representation are introduced and some properties are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations Ammon, Martin Hollweck, Jakob Hössel, Tobias Wölfl, Katharina High Energy Physics - Theory General Relativity and Quantum Cosmology We define and compute the four-dimensional thermal $n$-point conformal block in the projection channel using oscillator representations on $\mathbb{S}^1_β\times \mathbb{S}^3$. This is done by evaluating a class of integrals over the homogeneous space $\mathbb{D}_4$ of the four-dimensional conformal group. We restrict ourselves to scalar external operators and scalar exchange. In the low-temperature limit, our result reduces correctly to the vacuum $(n+2)$-point block in the comb channel. The corresponding expressions can be written as a series of terminating hypergeometric functions or equivalently, a series of weighted SU(2) spin-networks. Alternatively, functions adapted to the SU(2,2) representation are introduced and some properties are discussed. |
| title | Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2507.22974 |