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Explicit construction of the energy-momentum tensor in the large N limit

Carlo Pagani*

Hidenori Sonoda†

  • *Contact author: carlo.pagani@guest.ung.si
  • †Contact author: h-sonoda@pobox.com; Visiting Research Associate till 29 September 2026
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Phys. Rev. D 113, 025012 – Published 23 January, 2026

DOI: https://doi.org/10.1103/sfkr-vjkj

Abstract

We construct the energy-momentum tensor of the O(N) linear sigma model explicitly in the large N limit using the exact renormalization group (ERG) formalism. The energy-momentum tensor is obtained as a cutoff dependent functional of N scalar field variables. Our guiding principles behind the construction are twofold: first the energy-momentum tensor must satisfy the Ward identity for translation and rotation invariance, and second the energy-momentum tensor must satisfy a variant of the exact renormalization group equation. In the limit that the momentum cutoff goes to zero, our energy-momentum tensor gives the one-particle irreducible (1PI) effective action with the insertion of a single energy-momentum tensor operator. We verify that the energy-momentum tensor constructed satisfies the expected trace formula, and that the trace vanishes at the Wilson-Fisher critical point.

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Phys. Rev. D 113, 025012– Published 23 January, 2026
  • Received 24 August 2025
  • Accepted 6 January 2026
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