Curvature-squared invariants of minimal five-dimensional supergravity from superspace

Boundary terms and conserved charges in higher-derivative gauged supergravity

“…In [21] we gave a rather simple action for the bosonic sector of four-derivative minimal gauged supergravity, where the dynamical fields are the metric g µν and an Abelian gauge field A µ , and the four-derivative couplings are treated as a perturbation controlled by a parameter α with the dimension of a length squared. This action was obtained by starting from off-shell supergravity coupled to higher-derivative supersymmetric invariants [24,33,41,42], integrating out the auxiliary fields and using field redefinitions to simplify the result (see also [25][26][27][28] for related results). These manipulations were performed at linear order in α, so the final result is supersymmetric up to higher-order terms.…”

Hyper-dilaton Weyl multiplet of 4D, $$ \mathcal{N} $$ = 2 conformal supergravity

“…There are models of supergravity in conformal superspace in which the component reduction process and other relevant operations that are prerequisite to gauge fixing are either extremely repetitive or computationally so daunting that computer algebra systems are likely mandatory. For example, this is especially true when analyzing higher-derivative supergravities, which is the main topic of the recent works [19,17,18] of which our current paper largely refers, but the same is true for several of the works [6,11,29,10,19,17,18,13] where analogue computer algebra softwares were largely employed.…”

“…We proceed with an overview of the computational methodology when reducing superfields to components in 5D, N = 1 matter-coupled supergravity. For the mathematical and theoretical background behind the superspace expressions defined here and the physical relevance and application of all resulting component expressions, we refer the reader to [18,19]. For lack of space, we do not review all of the 5D N = 1 conformal superspace building blocks of [9,18,19].…”

“…This goes by the name of conformal superspace, which was first introduced by Daniel Butter for 4D, N = 1 supergravity [5] and later extended to different space-time dimensions and amount of supersymmetries -we refer the reader to the following references [27,26] for pedagogical reviews and a complete list of references. In the last decade, this approach has allowed to obtain many new results pushing forward a systematic analysis of higher-derivative supergravity by using off-shell techniques, as exemplified in the results in the following incomplete list of papers [7,8,12,9,25,6,11,29,10,19,17,18,13].…”

“…In this paper, we aim to give an overview of how supergravity component reduction (and other relevant operations) are performed by employing cadabra. Our focus is on presenting key aspects of the algorithms used to obtain the results that appeared in our recent works [19,17,18]. We also introduce a public repository [20] that can handle component reduction, derivative degauging, consistency checks, and more in 5D, N = 1 and 4D, N = 2 supergravity.…”