Type IIB Potential Gauge Transformations

On a contractible smooth patch, let ${\zeta }_1,{\mathrm{\Lambda }}_1,{\mathrm{\Lambda }}_3$ be smooth real gauge-parameter forms of degrees $1,1,3$. With the raw and tilded fields of Type IIB Two Derivative Supergravity Pseudoaction, define

$B_2^{\mathrm{\prime }}=B_2+d{\zeta }_1,C_0^{\mathrm{\prime }}=C_0,C_2^{\mathrm{\prime }}=C_2+d{\mathrm{\Lambda }}_1,C_4^{\mathrm{\prime }}=C_4+d{\mathrm{\Lambda }}_3-\frac{1}{2}{H}_3\wedge {\mathrm{\Lambda }}_1+\frac{1}{2}{G}_3\wedge {\zeta }_1\mathrm{.}$

The associated field strengths are those defined in Type IIB Two Derivative Supergravity Pseudoaction. The local transformation maps are definitions; their invariance consequence is established separately after this definition.

Type IIB Two Derivative Supergravity Pseudoaction

Hamilton, §7.1, generalized gauge transformations

The theorem proves invariance of the field strengths. Invariance of the full pseudoaction up to boundary terms is not asserted here; it requires a separate check of the Chern–Simons transformation and boundary conditions.

The gauge-parameter component dimensions are $[{\zeta }_M]=[{\mathrm{\Lambda }}_M]=[{\mathrm{\Lambda }}_{MNP}]=L$. Since a coordinate derivative has dimension $L^{-1}$ and the potential components are dimensionless under the adopted conventions, each component of $d{\zeta }_1$, $d{\mathrm{\Lambda }}_1$, $d{\mathrm{\Lambda }}_3$, $H_3\wedge {\mathrm{\Lambda }}_1$, and $G_3\wedge {\zeta }_1$ is dimensionless, as required by the shifts of $B_2,C_2,C_4$.