Correlation Functions and Trace Anomalies in Weakly Relevant Flows
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| Format: | Preprint |
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2024
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| author | Karateev, Denis Sahoo, Biswajit |
| author_facet | Karateev, Denis Sahoo, Biswajit |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_16825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Correlation Functions and Trace Anomalies in Weakly Relevant Flows Karateev, Denis Sahoo, Biswajit High Energy Physics - Theory 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. |
| title | Correlation Functions and Trace Anomalies in Weakly Relevant Flows |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.16825 |