Leonidas Karageorgos | Searcharxiv

arXiv2025

Energy momentum tensor correlators in $ϕ^4$ theory II: The spin-two sector

We extend the computation of the C_T charge of the 2-point function of the Energy-Momentum Tensor to 4-loops. We show that C_T decomposes into two sectors, the conformal sector, which encodes the value of the central charge at fixed points and an RG-sector that contains logarithmic and constant corrections proportional to the beta-function. This latter constitutes the main new result of this work and is inaccessible via CFT methods alone. Furthermore, we demonstrate that C_T satisfies an eigenvalue-like equation analogous to that of the spin-0 charge, as discussed in part I, though with a different in general eigenvalue. Finally we present three possible applications.

hep-th↗

arXiv2024

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

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.

hep-th↗