Energy-Momentum tensor correlators in $ϕ^4$ theory I: The spin-zero sector

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Irges, Nikos, Karageorgos, Leonidas
Format: Preprint
Publié: 2024
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866913562259095552
author Irges, Nikos
Karageorgos, Leonidas
author_facet Irges, Nikos
Karageorgos, Leonidas
contents We revisit the construction of the renormalized trace $Θ$ of the Energy-Momentum tensor in the four-dimensional $λϕ^4$ theory,using dimensional regularization in $d=4-\ve$ dimensions. We first construct several basic correlators such as $\braket{ϕ^2 ϕϕ}$, $\braket{ϕ^4 ϕϕ}$ to order $λ^2$ and from these the correlators $\braket{K_I ϕϕ}$ and $\braket{K_I K_J}$ with $K_I$ the basis of dimension $d$ operators. We then match the limit of their expressions on the Wilson-Fisher fixed point to the corresponding expressions obtained in Conformal Field Theory. Then, using the 3-point function $\braket{Θϕϕ}$, we construct the operator $Θ$ as a certain linear combination of the basis operators, using the requirements that $Θ$ should vanish on the fixed point and that it should have zero anomalous dimension. Finally, we compute the 2-point function $\braket{ΘΘ}$ and we show that it obeys an eigenvalue equation that gives additional information about the internal structure of the Energy-Momentum tensor operator to what is already contained in its Callan-Symanzik equation.
format Preprint
id arxiv_https___arxiv_org_abs_2410_16040
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Energy-Momentum tensor correlators in $ϕ^4$ theory I: The spin-zero sector
Irges, Nikos
Karageorgos, Leonidas
High Energy Physics - Theory
High Energy Physics - Phenomenology
We revisit the construction of the renormalized trace $Θ$ of the Energy-Momentum tensor in the four-dimensional $λϕ^4$ theory,using dimensional regularization in $d=4-\ve$ dimensions. We first construct several basic correlators such as $\braket{ϕ^2 ϕϕ}$, $\braket{ϕ^4 ϕϕ}$ to order $λ^2$ and from these the correlators $\braket{K_I ϕϕ}$ and $\braket{K_I K_J}$ with $K_I$ the basis of dimension $d$ operators. We then match the limit of their expressions on the Wilson-Fisher fixed point to the corresponding expressions obtained in Conformal Field Theory. Then, using the 3-point function $\braket{Θϕϕ}$, we construct the operator $Θ$ as a certain linear combination of the basis operators, using the requirements that $Θ$ should vanish on the fixed point and that it should have zero anomalous dimension. Finally, we compute the 2-point function $\braket{ΘΘ}$ and we show that it obeys an eigenvalue equation that gives additional information about the internal structure of the Energy-Momentum tensor operator to what is already contained in its Callan-Symanzik equation.
title Energy-Momentum tensor correlators in $ϕ^4$ theory I: The spin-zero sector
topic High Energy Physics - Theory
High Energy Physics - Phenomenology
url https://arxiv.org/abs/2410.16040