Dimensional uplifts of thermal two-point functions and higher-derivative CFTs
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≠ 0 the uplifted correlators are identified as two-point functions of a higher-derivative nonunitary thermal CFTd+2, but they differ from the uplifted nontrivial thermal two-point functions of the original unitary CFTd.
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BibTeX
@misc{li2026dimensional,
title = {{Dimensional uplifts of thermal two-point functions and higher-derivative CFTs}},
author = {Songyuan Li and Anastasios C. Petkou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08925},
eprint = {2610.08925},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08925},
}
RIS
TY - UNPB
TI - Dimensional uplifts of thermal two-point functions and higher-derivative CFTs
AU - Songyuan Li
AU - Anastasios C. Petkou
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08925
UR - https://arxiv.org/abs/2610.08925
AB - 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≠ 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.
ER -