2024/08/29 by Karateev, Denis, Sahoo, Biswajit · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2408.16825
We study abstract weakly relevant flows in a general number of dimensions. They arguably provide the simplest example of renormalization group (RG) flows between two non-trivial fixed points. We compute several two-point correlation functions in position space valid along the whole RG flow. This is done by using conformal perturbation theory together with the solution of the Callan-Symanzik equation. From the explicit expressions of the two-point functions of conserved currents and the stress-tensor we extract the change in the central charges between the UV and IR fixed points. This immediately gives us Δc, the change of the c-trace anomaly between the UV and IR fixed points in 4d. We also discuss three-point functions. We couple weakly relevant flows to non-dynamical dilaton and graviton background fields in 4d. We compute the three-dilaton vertex in terms of the scalar two-point function and extract the value of Δa, the change of the a-trace anomaly between the UV and IR fixed points. We also compute the graviton-graviton-dilaton vertex in terms of the three-point function of two stress-tensors and a scalar, and extract the value of Δc. The Δc values obtained with the two different methods agree.