Manuscript XVI-O@o70-sync · XVI-O.tex · lemma · bed49f2f

Lemma

Massless scalar matter loop · lines 208–224

XVI-O@o70-sync#lem:d11-prefactor, XVI-O@o70-sync#eq:pi-prefactor

Gate 2 normalizes the D11 prefactor. Route A, the Wick route, independently yields

lo g Z_{bubble} = - \frac{κ ^{2}}{8} \int h T h,

with $Γ_{1, matter} = - i lo g Z$ and $Π_{bubble} = (i κ^{2} /4) V V (C C + C C)$ . Route B expands $lo g Z = - \frac{1}{2} Tr lo g H$ to $(- κ^{2} /4) Tr (D_{F} H_{1} D_{F} H_{1})$ . Symmetry of $a_{1}$ gives $comb_{B} = \frac{1}{2}$ , which is Constructed and not unresolved, and

Π_{B} = \frac{i κ ^{2}}{4} T .

The tensor witness is $T_{0000} = 24 A^{2} / r^{8}$ at $z = (0, r, 0, 0)$ . That witness is corroboration of the stated point, not a universal identity by sampling.

Displayed formulas in this passage

XVI-O@o70-sync#eq:pi-prefactor · line 218
$Π_{B} = \frac{i κ ^{2}}{4} T .$
unlabeled · line 212
$lo g Z_{bubble} = - \frac{κ ^{2}}{8} \int h T h,$

Lemma

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