Manuscript Oai282-A@1 · Oai282-A.tex · section · 5b6134ec

An explicit affine superpotential

Stage 2: conditional improvement and its affine charges › An explicit affine superpotential · lines 671–690

Oai282-A@1#eq:affine-superpotential

For an affine Killing field

X^{μ} = a^{μ} + ω^{μ}_{ρ} x^{ρ}, ω_{μ ρ} = - ω_{ρ μ},

define

A_{ρ μν} [L] = \frac{1}{3} (η_{ρ ν} \partial_{μ} L - η_{μν} \partial_{ρ} L),

B_{ρ μ} [X, L] = X^{ν} A_{ρ μν} [L] + \frac{1}{3} (\partial_{ρ} X_{μ}) L .

Displayed formulas in this passage

Oai282-A@1#eq:affine-superpotential · line 684
$B_{ρ μ} [X, L] = X^{ν} A_{ρ μν} [L] + \frac{1}{3} (\partial_{ρ} X_{μ}) L .$
unlabeled · line 674
$X^{μ} = a^{μ} + ω^{μ}_{ρ} x^{ρ}, ω_{μ ρ} = - ω_{ρ μ},$
unlabeled · line 679
$A_{ρ μν} [L] = \frac{1}{3} (η_{ρ ν} \partial_{μ} L - η_{μν} \partial_{ρ} L),$