Tables (8)

Table p. 43.0 — 4×9, 0 spanning cell(s)
\(d\)01234567
\(\epsilon\)1-1111-111
\(\epsilon^{\prime}\)11-1-1-1-111
\(\epsilon^{\prime \prime}\)1-11-1

columns: \(d\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7

Table p. 181.1 — 6×3, 0 spanning cell(s)
\(D=3\) CS LagrangiansCharacteristic classesGroups
\[ L_{3}^{(A) d S}=\epsilon_{a b c}\left(R^{a b} \pm \frac{e^{a} e^{b}}{3 l^{2}}\right) e^{c} \]\(\mathbf{E}_{4}=\epsilon_{a b c}\left(R^{a b} \pm \frac{e^{a} e^{b}}{l^{2}}\right) T^{c}\)\begin{tabular}[t]{l} \(S O(4)\), \\ \(S O(3,1)\) \\ or \(S O(2,2)\) \end{tabular}
\(L_{3}^{\text {Lor }}=\omega^{a}{ }_{b} d \omega^{b}{ }_{a}+\frac{2}{3} \omega^{a}{ }_{b} \omega^{b}{ }_{c} \omega^{c}{ }_{a}\)\(\mathbf{P}_{4}^{\text {Lor }}=R^{a}{ }_{b} R^{b}{ }_{a}\)\(S O(2,1)\)
\(L_{3}^{T o r}=e^{a} T_{a}\)\(\mathbf{N}_{4}=T^{a} T_{a}-e^{a} e^{b} R_{a b}\)\(S O(2,1)\)
\(L_{3}^{U(1)}=A d A\)\(\mathbf{P}_{4}^{U(1)}=F F\)\(U(1)\)
\(L_{3}^{S U(N)}=\operatorname{Tr}\left[\mathbf{A} d \mathbf{A}+\frac{2}{3} \mathbf{A} \mathbf{A} \mathbf{A}\right]\)\(\mathbf{P}_{4}^{S U(4)}=\operatorname{Tr}[\mathbf{F F}]\)\(S U(N)\)

columns: \(D=3\) CS Lagrangians | Characteristic classes | Groups

Table p. 182.2 — 4×2, 0 spanning cell(s)
\(D=7 \mathrm{CS}\) LagrangiansCharacteristic classes
\(L_{7}^{\text {Lor }}=\omega(d \omega)^{3}+\frac{8}{5} \omega^{3}(d \omega)^{2}+\cdots+\frac{4}{7} \omega^{7}\)\(\mathbf{P}_{8}^{\text {Lor }}=R^{a}{ }_{b} R^{b}{ }_{c} R^{c}{ }_{d} R^{d}{ }_{a}\)
\(L_{7}^{I}=\left(\omega^{a}{ }_{b} d \omega^{b}{ }_{a}+\frac{2}{3} \omega^{a}{ }_{b} \omega^{b}{ }_{c} \omega^{c}{ }_{a}\right) R^{a}{ }_{b} R^{b}{ }_{a}\)\(\left(\mathbf{P}_{4}^{\text {Lor }}\right)^{2}=\left(R^{a}{ }_{b} R^{b}{ }_{a}\right)^{2}\)
\(L_{7}^{I I}=\left(e^{a} T_{a}\right)\left(R^{a}{ }_{b} R^{b}{ }_{a}\right)\)\[ \begin{aligned} & \mathbf{N}_{4} \mathbf{P}_{4}^{\text {Lor }}= \\ & \left(T^{a} T_{a}-e^{a} e^{b} R_{a b}\right) R^{c}{ }_{d} R^{d}{ }_{c} \end{aligned} \]

columns: \(D=7 \mathrm{CS}\) Lagrangians | Characteristic classes

Table p. 205.3 — 4×9, 0 spanning cell(s)
n01234567
\(\varepsilon\)11-1-1-1-111
\(\varepsilon^{\prime}\)1-1111-111
\(\varepsilon^{\prime \prime}\)1-11-1

columns: n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7

Table p. 281.4 — 2×2, 0 spanning cell(s)
\(L\)\(p p p p\)
k \(k k\) k\(\bar{L}\)

columns: \(L\) | \(p p p p\)

Table p. 281.5 — 3×3, 0 spanning cell(s)
\(L\)\(P\)\(Q\)
\(K\)\(L\)\(S\)
\(S\)\(\bar{Q}\)\(R\)

columns: \(L\) | \(P\) | \(Q\)

Table p. 286.6 — 2×2, 0 spanning cell(s)
\(L\)\(p p p p\)
k \(k k k\)\(\bar{L}\)

columns: \(L\) | \(p p p p\)

Table p. 287.7 — 2×2, 0 spanning cell(s)
\(\mathfrak{s} \mathfrak{u}(2 \mid 2)\)create \(8_{B}+8_{F}\) magnons
destroy 8 + 8 magnons\(\overline{\mathfrak{s} \mathfrak{u}(2 \mid 2)}\)

columns: \(\mathfrak{s} \mathfrak{u}(2 \mid 2)\) | create \(8_{B}+8_{F}\) magnons