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arXiv:2610.08925

Dimensional uplifts of thermal two-point functions and higher-derivative CFTs

Songyuan Li, Anastasios C. Petkou

Published Oct 6, 2026• 0 citations
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Abstract

We explore the idea that the mass parameter $m$ can be used as a diagnostic tool for identifying the critical points of thermal two-point functions of massive free scalar fields in odd $d$ dimensions. For general values of $m$ these correlators admit an expansion in thermal conformal blocks associated with symmetric traceless operators of definite scaling dimension. For each spin the higher-twist contributions can be resummed into a closed-form dressing factor of the leading-twist coefficient. At special values of $m$ for which the thermal trace of the energy-momentum tensor vanishes they are identified as two-point functions of thermal CFTs. Through a dimensional uplift, valid for all $m$, we map these correlators to thermal two-point functions of higher-derivative massive theories in $d+2$ dimensions. We show that the thermal trace of the energy-momentum tensor of the $d+2$-dimensional theory is proportional to the free energy of the original $d$-dimensional theory. When that thermal trace vanishes for $m\neq 0$ the uplifted correlators are identified as two-point functions of a higher-derivative nonunitary thermal CFT$_{d+2}$, but they differ from the uplifted nontrivial thermal two-point functions of the original unitary CFT$_d$.

DOI
10.48550/arxiv.2610.08925

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