nLab parent action functional

Idea

In physics one speakes of a parent action functional (Deser-Jackiw 84) when referring to an action functional $S_{par}$ which, by solving the equations of motion of two different sets of its “auxiliary” fields, is classically equivalent to two different-looking action functionals $S_A$ and $S_B$, thereby exhibiting $S_A$ and $S_B$ as classically equivalent to each other. Hence a parent action functional constitutes a correspondence between two action functionals

$$\array{ && S_{par} \\ & {}^{\mathllap{\simeq_{clas}}}\swarrow && \searrow^{\mathrlap{\simeq_{clas}}} \\ S_A && && S_B } \,.$$

The method is used notably to exhibit “duality” between $S_A$ and $S_B$ of one form or another, in particular electric-magnetic duality. (See e.g. Miao-Ohta 03).

Beware that some authors also speak of master actions instead of parent actions in this context, but there is not relation to “master actions” in the sense of BV-BRST formalism (except, of course, that both are action functionals of some sort).

References

• Stanley Deser, Roman Jackiw, Phys. Lett. B, 139 (1984), p. 2366

• Yan-Gang Miao, Nobuyoshi Ohta, Parent Actions, Dualities and New Weyl-invariant Actions of Bosonic p-branes (arXiv:hep-th/0301233)