Thermodynamics in symmetry-improved Cornwall-Jackiw-Tomboulis formalism: application to the low-energy effective theory of QCD
Abstract
We study the thermodynamics of the symmetry-improved Cornwall-Jackiw-Tomboulis (SICJT) formalism and apply it to a low-energy effective theory of QCD. In the symmetry-improved formulation, Ward-Takahashi identities are restored by auxiliary sources whose values are fixed self-consistently by the equilibrium state. While this construction improves the symmetry properties of the loop-wise truncated two-particle-irreducible (2PI) theory, it also makes the thermodynamic interpretation of the pressure nontrivial. We formulate several pressure prescriptions, including the conventional vacuum-subtracted pressure, a source-matched subtraction, and a pulled-back pressure in which the explicit source-induced energy shift is removed. Using the three-flavor linear sigma model with quarks, we analyze the equation of state, isentropic trajectories, adiabatic sound velocity, and trace anomaly across the chiral transition. We find that the global thermodynamic structure is stable under the different prescriptions, while quantitative differences are concentrated near the crossover and first-order transition region. These results establish a practical framework for constructing thermodynamically consistent observables in symmetry-improved 2PI approaches.
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BibTeX
@misc{guan2026thermodynamics,
title = {{Thermodynamics in symmetry-improved Cornwall-Jackiw-Tomboulis formalism: application to the low-energy effective theory of QCD}},
author = {Yuepeng Guan and Mamiya Kawaguchi and Shinya Matsuzaki and Akio Tomiya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.29701},
eprint = {2605.29701},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.29701},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Thermodynamics in symmetry-improved Cornwall-Jackiw-Tomboulis formalism: application to the low-energy effective theory of QCD
AU - Yuepeng Guan
AU - Mamiya Kawaguchi
AU - Shinya Matsuzaki
AU - Akio Tomiya
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2605.29701
UR - https://arxiv.org/abs/2605.29701
AB - We study the thermodynamics of the symmetry-improved Cornwall-Jackiw-Tomboulis (SICJT) formalism and apply it to a low-energy effective theory of QCD. In the symmetry-improved formulation, Ward-Takahashi identities are restored by auxiliary sources whose values are fixed self-consistently by the equilibrium state. While this construction improves the symmetry properties of the loop-wise truncated two-particle-irreducible (2PI) theory, it also makes the thermodynamic interpretation of the pressure nontrivial. We formulate several pressure prescriptions, including the conventional vacuum-subtracted pressure, a source-matched subtraction, and a pulled-back pressure in which the explicit source-induced energy shift is removed. Using the three-flavor linear sigma model with quarks, we analyze the equation of state, isentropic trajectories, adiabatic sound velocity, and trace anomaly across the chiral transition. We find that the global thermodynamic structure is stable under the different prescriptions, while quantitative differences are concentrated near the crossover and first-order transition region. These results establish a practical framework for constructing thermodynamically consistent observables in symmetry-improved 2PI approaches.
ER -