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Properties of scalar partition functions of 2d CFTs

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arxiv 2505.18314 v1 pith:KEH5CI3R submitted 2025-05-23 hep-th

Properties of scalar partition functions of 2d CFTs

classification hep-th
keywords functionpartitionscalarconformalequationfieldmodularnontrivial
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study the spectrum of scalar primary operators in any two-dimensional conformal field theory. We show that the scalars alone obey a nontrivial crossing equation. This extends previous work that derived a similar equation for Narain conformal field theories. Additionally, we show that at high temperature, the difference between the true scalar partition function and the one predicted from a semiclassical gravity calculation is controlled by: the modular integral of the partition function, the light states of the theory, and an infinite series terms directly related to the nontrivial zeros of the Riemann zeta function. We give several numerical examples and compute their modular integrals.

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    TTbar-deformed CFT torus partition functions are expressed via spectral decomposition into Maass forms that deform simply, enabling analytic continuation beyond the Hagedorn singularity.