The OPE Approach to Renormalization: Operator Mixing
TLDR
This paper extends OPE-based renormalization to composite operators with mixing, providing a recursive framework and calculating anomalous dimensions.
Key contributions
- Extends OPE-based renormalization to composite operators with operator mixing.
- Develops a recursive renormalization framework using OPE coefficients of lower-dimensional tensors.
- Calculates five-loop anomalous dimensions for operators with Δ≤5 in the φ⁴ model.
- Reports two-loop anomalous dimensions for operators with Δ≤10 in the φ³ model.
Why it matters
This work significantly advances quantum field theory by providing a more versatile and efficient renormalization algorithm for composite operators. The new recursive framework and high-loop anomalous dimension calculations demonstrate its power, opening new avenues for theoretical physics research.
Original Abstract
We extend the OPE-based renormalization algorithm to composite operators with operator mixing, focusing on scalar operators in $φ^4$ and $φ^3$ models. Using the OPE of operators with a fundamental field, we show that the $Z$-factors of these composite operators are determined by OPE coefficients of lower-dimensional traceless symmetric tensor operators, and establish a recursive renormalization framework. We report the five-loop anomalous dimensions for operators with $Δ\le5$ in the $φ^4$ model and the two-loop anomalous dimensions for operators with $Δ\le10$ in the $φ^3$ model. These results further demonstrate the versatility and efficiency of the OPE-based algorithm.
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