The Universal RG Machine

Details The Universal RG Machine The Universal RG Machine

2010-12-14

arxiv.org/abs/1012.3081v1

JHEP 1106 (2011) 079

Physics

High Energy Physics

High Energy Physics - Theory

38 pages

Scientific paper

10.1007/JHEP06(2011)079

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.

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