Abstract
We study the 2d chiral Gross-Neveu model at finite temperature T and chemical potential μ. The analysis is performed by relating the theory to a SU(N) × U(1) Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At μ = 0 we show that a certain ℤ2-valued ’t Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any N and any T > 0. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for T > 0 of the inhomogeneous chiral phase configuration found at T = 0 for any N and any μ. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for T > 0 and any μ for periodic fermions, as expected from anomaly considerations. A large N analysis confirms the above findings.
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Acknowledgments
We thank Andrea Antinucci, Francesco Benini, Christian Copetti, Pavel Putrov, Ryan Thorngren and Jingxiang Wu for discussions. MS thanks the Institut des Hautes Études Scientifiques (IHES), where part of this work has been done, for the hospitality. Work partially supported by INFN Iniziativa Specifica ST&FI.
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Ciccone, R., Di Pietro, L. & Serone, M. Anomalies and persistent order in the chiral Gross-Neveu model. J. High Energ. Phys. 2024, 211 (2024). https://doi.org/10.1007/JHEP02(2024)211
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DOI: https://doi.org/10.1007/JHEP02(2024)211