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

TL;DR

This paper explicitly constructs the energy-momentum tensor for the O(N) linear sigma model in the large N limit using the ERG formalism, ensuring it satisfies Ward identities and the RG equation.

Contribution

It provides a novel explicit construction of the energy-momentum tensor in the large N limit within the ERG framework, satisfying key physical and mathematical constraints.

Findings

The constructed tensor satisfies Ward identities for translation and rotation invariance.

It reproduces the 1PI effective action with energy-momentum insertion in the zero cutoff limit.

The trace of the tensor vanishes at the Wilson-Fisher critical point.

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.