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 β-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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- June 2011
- DOI:
- 10.1007/JHEP06(2011)079
- arXiv:
- arXiv:1012.3081
- Bibcode:
- 2011JHEP...06..079B
- Keywords:
-
- Models of Quantum Gravity;
- Renormalization Group;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 38 pages