The Universal RG Machine
Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig

TL;DR
The paper introduces a systematic algorithm using off-diagonal heat-kernel techniques to compute functional renormalization group equations, enabling complex calculations in theories like gravity and Yang-Mills.
Contribution
It presents a novel computational method for deriving flow equations in quantum field theories, applicable to background-independent scenarios.
Findings
Re-derivation of gravitational beta-functions demonstrating background-independence
Development of a computer-implementable algorithm for flow equation expansion
Calculation of heat-kernel coefficients for specific tensor fields to second order in curvature
Abstract
Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational -functions of the Einstein-Hilbert truncation, demonstrating their background-independence. As an additional result, the heat-kernel coefficients for transverse vectors and transverse-traceless symmetric matrices are computed to second order in the curvature.
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