We study the $2d$ chiral Gross-Neveu model at finite temperature $T$ and chemical potential $\mu$. The analysis is performed by relating the theory to a $SU(N)\times U(1)$ Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At $\mu=0$ we show that a certain $\mathbb{Z}_2$-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 $\mu$. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for $T>0$ and any $\mu$ for periodic fermions, as expected from anomaly considerations. A large $N$ analysis confirms the above findings.

Anomalies and Persistent Order in the Chiral Gross-Neveu model / Ciccone, Riccardo; Di Pietro, Lorenzo; Serone, Marco. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2024:(2024), pp. 1-50. [10.1007/JHEP02(2024)211]

Anomalies and Persistent Order in the Chiral Gross-Neveu model

Riccardo Ciccone
;
Lorenzo Di Pietro
;
Marco Serone
2024-01-01

Abstract

We study the $2d$ chiral Gross-Neveu model at finite temperature $T$ and chemical potential $\mu$. The analysis is performed by relating the theory to a $SU(N)\times U(1)$ Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At $\mu=0$ we show that a certain $\mathbb{Z}_2$-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 $\mu$. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for $T>0$ and any $\mu$ for periodic fermions, as expected from anomaly considerations. A large $N$ analysis confirms the above findings.
2024
2024
1
50
211
http://arxiv.org/abs/2312.13756v2
Ciccone, Riccardo; Di Pietro, Lorenzo; Serone, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/136932
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