Finite-temperature operator basis on ℝ3 × S1 for SMEFT
Abstract
We present the first complete non-redundant operator basis for the Standard Model Effective Field Theory (SMEFT) at finite temperature, using the imaginary-time formalism. By employing the Hilbert series method on the space-time manifold ℝ3 × S1, we classify all effective operators up to dimension-six. In constructing the basis, we consistently impose integration-by-parts and equations-of-motion constraints along spatial directions. We further analyze the impact of additional constraints, including the vanishing of the curl of the electric and magnetic fields and gauge choices for the temporal components on an operator basis. We also realize them in terms of static three-dimensional spatial and zero-temperature SMEFT operators. At dimension five and six, we identify intrinsically thermal operators that vanish with temperature. Our framework is fully general and extends to arbitrary mass dimension and compact connected internal symmetry groups.
Versions
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BibTeX
@misc{chakrabortty2026finitetemperature,
title = {{Finite-temperature operator basis on $\mathbbR^3 \times S^1$ for SMEFT}},
author = {Joydeep Chakrabortty and Bruno Siqueira Eduardo and Siddhartha Karmakar and Philipp Schicho},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.02878},
eprint = {2605.02878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02878},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Finite-temperature operator basis on ℝ^3 × S^1 for SMEFT
AU - Joydeep Chakrabortty
AU - Bruno Siqueira Eduardo
AU - Siddhartha Karmakar
AU - Philipp Schicho
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2605.02878
UR - https://arxiv.org/abs/2605.02878
AB - We present the first complete non-redundant operator basis for the Standard Model Effective Field Theory (SMEFT) at finite temperature, using the imaginary-time formalism. By employing the Hilbert series method on the space-time manifold ℝ^3 × S^1, we classify all effective operators up to dimension-six. In constructing the basis, we consistently impose integration-by-parts and equations-of-motion constraints along spatial directions. We further analyze the impact of additional constraints, including the vanishing of the curl of the electric and magnetic fields and gauge choices for the temporal components on an operator basis. We also realize them in terms of static three-dimensional spatial and zero-temperature SMEFT operators. At dimension five and six, we identify intrinsically thermal operators that vanish with temperature. Our framework is fully general and extends to arbitrary mass dimension and compact connected internal symmetry groups.
ER -