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There are 5 irreducible bubbles that contribute to the A function at this order A(2) =a2,a +a2,b +a2,c +a2,d +a2,e

As in the one loop case υ(2) ij = 0 because it is impossible to form antisymmetric contractions also at order g4, which means that β(2) = B(2)

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Gradient properties of $\varphi^3$ in $d=6-\varepsilon$

hep-th · 2025-07-28 · conditional · novelty 6.0

The d = 6 gradient (A-function) structure of the phi^3 RG flow extends to d = 6 − epsilon, requiring one new three-loop constraint, Eq. (22), that the MS coefficients satisfy.

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  • Gradient properties of $\varphi^3$ in $d=6-\varepsilon$ hep-th · 2025-07-28 · conditional · none · ref 2

    The d = 6 gradient (A-function) structure of the phi^3 RG flow extends to d = 6 − epsilon, requiring one new three-loop constraint, Eq. (22), that the MS coefficients satisfy.