Energy-Momentum tensor correlators in $ϕ^4$ theory I: The spin-zero sector
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| 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 |