Fri - 08/01/25

**Title:

      Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations**  - **Authors:** Martin Ammon, Jakob Hollweck, Tobias Hössel, Katharina Wölfl  - **Subjects:** Subjects: High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  We define and compute the four-dimensional thermal $n$-point conformal block in the projection channel using oscillator representations on $\mathbb{S}^1_\beta \times \mathbb{S}^3$. 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.

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