From Z to a: High-temperature relations, subleading semi-universality, and conformal anomalies
Abstract
The free energy of any CFT, $ \ln Z(β; ω_i)$, admits two expansions: high temperature (β→ 0) and fast rotation (ωi → 1). We demonstrate that in 4d, locality of the thermal effective action forces ln Z to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order β1 due to the Weyl anomaly. From this, the a-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in β obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even d, but find no similar relations at odd d.
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BibTeX
@misc{advant2026from,
title = {{From $Z$ to $a$: High-temperature relations, subleading semi-universality, and conformal anomalies}},
author = {Arnav Advant and Harsh Anand and Nathan Benjamin and Vipul Kumar and Shiraz Minwalla and Jyotirmoy Mukherjee and Sridip Pal and Asikur Rahaman and Pabitra Ray},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03013},
eprint = {2609.03013},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05742731v1},
}
RIS
TY - UNPB
TI - From Z to a: High-temperature relations, subleading semi-universality, and conformal anomalies
AU - Arnav Advant
AU - Harsh Anand
AU - Nathan Benjamin
AU - Vipul Kumar
AU - Shiraz Minwalla
AU - Jyotirmoy Mukherjee
AU - Sridip Pal
AU - Asikur Rahaman
AU - Pabitra Ray
PY - 2026
DA - 2026/09/08
PB - HAL
DO - 10.48550/arxiv.2609.03013
UR - https://hal.science/hal-05742731v1
AB - The free energy of any CFT, $ \ln Z(β; ω_i)$, admits two expansions: high temperature (β→ 0) and fast rotation (ω_i → 1). We demonstrate that in 4d, locality of the thermal effective action forces ln Z to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order β^1 due to the Weyl anomaly. From this, the a-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in β obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even d, but find no similar relations at odd d.
ER -