Explicit construction of the energy-momentum tensor in the large N limit of a four-Fermi theory
Abstract
Using the exact renormalization group (functional RG) formalism, we construct the energy-momentum tensor of a four-Fermi theory in the Euclidean space of dimensions 2 < D < 4 in the large N limit, where N is the number of Dirac fields. The energy-momentum tensor is a functional of the Dirac fields, and its cutoff dependence is controlled by the exact RG equation. In the zero cutoff limit the functional reduces to the one-particle-irreducible effective action with a single insertion of the energy-momentum tensor. At a finite cutoff the energy-momentum tensor satisfies the Ward-Takahashi identity for translation invariance, and its antisymmetric part is determined by rotation invariance. We also show that the critical theory is conformally invariant by deriving the corresponding Ward-Takahashi identity.
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BibTeX
@misc{pagani2026explicit,
title = {{Explicit construction of the energy-momentum tensor in the large N limit of a four-Fermi theory}},
author = {Carlo Pagani and Hidenori Sonoda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20054},
eprint = {2609.20054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20054},
}
RIS
TY - UNPB
TI - Explicit construction of the energy-momentum tensor in the large N limit of a four-Fermi theory
AU - Carlo Pagani
AU - Hidenori Sonoda
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20054
UR - https://arxiv.org/abs/2609.20054
AB - Using the exact renormalization group (functional RG) formalism, we construct the energy-momentum tensor of a four-Fermi theory in the Euclidean space of dimensions 2 < D < 4 in the large N limit, where N is the number of Dirac fields. The energy-momentum tensor is a functional of the Dirac fields, and its cutoff dependence is controlled by the exact RG equation. In the zero cutoff limit the functional reduces to the one-particle-irreducible effective action with a single insertion of the energy-momentum tensor. At a finite cutoff the energy-momentum tensor satisfies the Ward-Takahashi identity for translation invariance, and its antisymmetric part is determined by rotation invariance. We also show that the critical theory is conformally invariant by deriving the corresponding Ward-Takahashi identity.
ER -