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arXiv · 2603.13469

Analytic structure of holographic thermal correlators from Fourier series

Paolo Arnaudo·Benjamin Withers
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Abstract

We compute the holographic Euclidean two-point function of scalar operators in a thermal state. We work directly using the Fourier series on the thermal circle. The Fourier series does not converge as a function, but instead converges as a distribution, consistent with QFT expectations. The result is manifestly periodic and consistent with analyticity in the strip $0<\mathfrak{Re}(\tau)<\beta$. Expanding in $\tau$ we obtain all OPE coefficients, including the double-trace sector. Thus our approach has an advantage compared to recent work where double-traces were bootstrapped from stress-tensor data. Bouncing singularities appear as non-perturbative sectors in the transseries for Fourier coefficients, but their transseries parameters are all zero in the case of the Euclidean correlator.

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Paolo Arnaudo, Benjamin Withers. 2026-03-13. Analytic structure of holographic thermal correlators from Fourier series. https://arxiv.org/abs/2603.13469

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