2010/12/14 by Dario Benedetti, Kai Groh, Pedro F. Machado +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Computation #ENCODE #Flow (mathematics) #Gravitation #Order (exchange) #Quantum and Classical Electrodynamics #Renormalization #Renormalization group #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep06(2011)079
published as JHEP 1106 (2011) 079 · 38 pages
arxiv created 2010/12/14 · openalex publication_date 2011/06/01 · arxiv updated 2011/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.