Universality and the Renormalisation Group

Abstract

Several functional renormalisation group (RG) equations including Polchinski flows and Exact RG flows are compared from a conceptual point of view and in given truncations. Similarities and differences are highlighted with special emphasis on stability properties. The main observations are worked out at the example of O(N) symmetric scalar field theories where the flows, universal critical exponents and scaling potentials are compared within a derivative expansion. To leading order, it is established that Polchinski flows and ERG flows - despite their inequivalent derivative expansions - have identical universal content, if the ERG flow is amended by an adequate optimisation. The results are also evaluated in the light of stability and minimum sensitivity considerations. Extensions to higher order and further implications are emphasized.

15 pages, 2 figures; paragraph after (19), figure 2, and references added

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• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
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• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
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• The fate of non-polynomial interactions in scalar field theory
• Generalized universality in the massive sine-Gordon model
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• Isotropic Lifshitz critical behavior from the functional renormalization group
• Towards Functional Flows for Hierarchical Models
• Phase Structure and Compactness
• Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
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• Critical and multicritical Lee-Yang fixed points in the local potential approximation