The Universal RG Machine

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 $\beta$-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.

38 pages

References in corpus (6)

• Asymptotic safety in higher-derivative gravity
• Ultraviolet properties of f(R)-Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Matter Induced Bimetric Actions for Gravity
• Improved Schwinger-DeWitt techniques for higher-derivative perturbations of operator determinants