Scheme invariants in phi^4 theory in four dimensions

Abstract

We provide an analysis of the structure of renormalisation scheme invariants for the case of ${\varphi }^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at five loops, showing that there are considerably more invariants than one might naively have expected. We also show that one-vertex reducible contributions may consistently be omitted in a well-defined class of schemes which of course includes MSbar.

Uses tikz; revised version with minor errors corrected

References in corpus (5)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• A challenge to the $a$-theorem in six dimensions
• The a-function in three dimensions: beyond leading order
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Cited by in corpus (4)

• General scalar renormalisation group equations at three-loop order
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• ARGES -- Advanced Renormalisation Group Equation Simplifier