PreprintCC BY 4.0arXiv
From Z to all: cyclic sum rules for thermal CFT partition functions
Abstract
The high-temperature expansion of twisted Sd−1× S1 partition functions of CFTd, d = 2κ, has recently been shown to obey an infinite tower of universal constraints. We determine these constraints explicitly and demonstrate that they can be packaged into a single equation involving a large conformal diffeomorphism isomorphic to ℤκ+1, which cyclically permutes the thermal circle and the rotation angles. Our equation asserts that the ℤκ+1-invariant part of ln Z/β is a constant fixed by the a-anomaly. Our derivation assumes CP-invariance and locality of the thermal effective action, whose structure we constrain using an algebraic formalism starting from embedding space.
Related
- Finding CFTs from spatial positivity of partition functions
- Trace Relations and Partition Functions
- Some universalities in the partition functions of low-dimensional gravity models
- AI estimation of partition functions with the PULSE method for the thermodynamic properties of disordered compounds
- Instantons from geometry in M2-brane sphere partition functions
BibTeX
@misc{advant2026from,
title = {{From Z to all: cyclic sum rules for thermal CFT partition functions}},
author = {Arnav Advant and Harsh Anand and Nathan Benjamin and Abhijit Gadde and Vipul Kumar and Shiraz Minwalla and Jyotirmoy Mukherjee and Sridip Pal and Asikur Rahaman and Pabitra Ray},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05281},
eprint = {2611.05281},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05281},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Z to all: cyclic sum rules for thermal CFT partition functions
AU - Arnav Advant
AU - Harsh Anand
AU - Nathan Benjamin
AU - Abhijit Gadde
AU - Vipul Kumar
AU - Shiraz Minwalla
AU - Jyotirmoy Mukherjee
AU - Sridip Pal
AU - Asikur Rahaman
AU - Pabitra Ray
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05281
UR - https://arxiv.org/abs/2611.05281
AB - The high-temperature expansion of twisted S^d−1× S^1 partition functions of CFT_d, d = 2κ, has recently been shown to obey an infinite tower of universal constraints. We determine these constraints explicitly and demonstrate that they can be packaged into a single equation involving a large conformal diffeomorphism isomorphic to ℤ_κ+1, which cyclically permutes the thermal circle and the rotation angles. Our equation asserts that the ℤ_κ+1-invariant part of ln Z/β is a constant fixed by the a-anomaly. Our derivation assumes CP-invariance and locality of the thermal effective action, whose structure we constrain using an algebraic formalism starting from embedding space.
ER -