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Scheme invariants in phi⁴ theory in four dimensions
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Scheme invariants in phi⁴ theory in four dimensions
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We provide an analysis of the structure of renormalisation scheme invariants for the case of $\phi^4$ 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.
Forward citations
Cited by 4 Pith papers
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Gradient RG Flow in Scalar-Fermion QFTs
RG flow in scalar-fermion theories is gradient through four loops only when the 'beta shift' is included, via over a thousand scheme-independent constraints that hold wherever current data allow a check.
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$\phi^6$ at $6$ (and some $8$) loops in $3d$
Six-loop beta-function graphs for general ϕ⁶ theory in 3d are recalculated (differing from Hager, agreeing with recent work), with large-N eight-loop results, O(ε³) exponents, and gradient-flow linear relations.
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$\phi^6$ at $6$ (and some $8$) loops in $3d$
Recalculation of individual six-loop graph contributions to the beta function in 3d phi^6 theory with arbitrary potential, plus large-N eight-loop terms and O(epsilon^3) critical exponents at the O(N) fixed point.
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$\phi^6$ at $6$ (and some $8$) loops in $3d$
Recalculation of individual six-loop graph contributions to the β-function in 3d φ⁶ theory with arbitrary potential, plus large-N eight-loop diagrams and O(ε³) critical exponents at the O(N) fixed point.
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