Manuscript XII-D@1 · XII-D.tex · input · 308a2080

Input statement: XII-C: the chosen action and source

Release criteria and copied inputs · lines 297–325

XII-D@1#eq:source-input

The selected model weights the specified cubic density only:

S_{grav, D} = S_{EH} + κ \int_{M_{T}} (σ_{ε} - 1) ℓ_{3} d^{4} x, ℓ_{3} = - 2 (r_{3} + b_{1} r_{2} + b_{2} r_{1}) .

The scalar action, free gauge-fixing coefficient, and higher unweighted gravitational coefficients are unchanged. The actual cubic Euler source is

J_{D}^{μν} = σ_{ε} J_{3}^{μν} + D_{σ}_{ε}^{μν}, D_{σ}_{ε}^{μν} = 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ_{ε} - 2 M_{2}^{μν ρ} \partial_{ρ} σ_{ε} .

In the pure-trace sector,

η_{μν} D_{σ}_{ε}^{μν}_{γ = ψ η} = - 6 (\partial_{μ} σ_{ε}) ψ \partial^{μ} ψ .

The layer coefficients are smooth and flat at their endpoints; they are not hypersurface distributions XIIC.

Displayed formulas in this passage

XII-D@1#eq:source-input · line 309
$J_{D}^{μν} = σ_{ε} J_{3}^{μν} + D_{σ}_{ε}^{μν}, D_{σ}_{ε}^{μν} = 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ_{ε} - 2 M_{2}^{μν ρ} \partial_{ρ} σ_{ε} .$
unlabeled · line 299
$S_{grav, D} = S_{EH} + κ \int_{M_{T}} (σ_{ε} - 1) ℓ_{3} d^{4} x, ℓ_{3} = - 2 (r_{3} + b_{1} r_{2} + b_{2} r_{1}) .$
unlabeled · line 319
$η_{μν} D_{σ}_{ε}^{μν}_{γ = ψ η} = - 6 (\partial_{μ} σ_{ε}) ψ \partial^{μ} ψ .$