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Journal Article

The universal RG machine


Benedetti,  Dario
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Benedetti, D., Groh, K., Machado, P. F., & Saueressig, F. (2011). The universal RG machine. Journal of High Energy Physics, 2011: 079. doi:10.1007/JHEP06(2011)079.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-D188-0
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.