Anomalies and Persistent Order in the Chiral Gross-Neveu model
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| Format: | Preprint |
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2023
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| _version_ | 1866916104147828736 |
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| author | Ciccone, Riccardo Di Pietro, Lorenzo Serone, Marco |
| author_facet | Ciccone, Riccardo Di Pietro, Lorenzo Serone, Marco |
| contents | 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 $SU(N)\times U(1)$ 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 $\mathbb{Z}_2$-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 $μ$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_13756 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anomalies and Persistent Order in the Chiral Gross-Neveu model Ciccone, Riccardo Di Pietro, Lorenzo Serone, Marco High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Phenomenology 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 $SU(N)\times U(1)$ 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 $\mathbb{Z}_2$-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 $μ$. 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. |
| title | Anomalies and Persistent Order in the Chiral Gross-Neveu model |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2312.13756 |