Superform formulation for vector-tensor multiplets in conformal supergravity

Abstract:We examine the five-dimensional super-de Rham complex with N = 1 supersymmetry. The elements of this complex are presented explicitly and related to those of the six-dimensional complex in N = (1, 0) superspace through a specific notion of dimensional reduction. This reduction also gives rise to a second source of five-dimensional supercocycles that is based on the relative cohomology of the two superspaces. In the process of investigating these complexes, we discover various new features including branching and fusion (loops) in the super-de Rham complex, a natural interpretation of "Weil triviality", p-cocycles that are not supersymmetric versions of closed bosonic p-forms, and the opening of a "gap" in the complex for D > 4 in which we find a multiplet of superconformal gauge parameters.

Section: Discussionmentioning

confidence: 99%

Superforms in five-dimensional, N = 1 superspace

Gates

Linch

Randall

2015

“…ref. [4,59,60]). Instead, we restrict our attention to the two applications that most overlap with the results already derived.…”

Section: Applicationsmentioning

confidence: 99%

Superforms in six-dimensional superspace

Arias

Linch

Ridgway

2016

Abstract:We investigate the complex of differential forms in curved, six-dimensional, N = (1, 0) superspace. The superconformal group acts on this complex by super-Weyl transformations. An ambi-twistor-like representation of a second conformal group arises on a pure spinor subspace of the cotangent space. The p-forms are defined by super-Weylcovariant tensor fields on this pure spinor subspace. The on-shell dynamics of such fields is superconformal. We construct the superspace de Rham complex by successively obstructing the closure of forms. We then extend the analysis to composite forms obtained by wedging together forms of lower degree. Finally, we comment on applications to integration in curved superspace and propose a superspace formulation of the abelian limit of the nonabelian tensor hierarchy of N = (1, 0) superconformal models.

“…See[77,78] for a superspace description of all known off-shell vector-tensor multiplets in 4D N = 2 conformal supergravity.…”

mentioning

confidence: 99%

Conformal supergravity in five dimensions: new approach and applications

Butter

Kuzenko

Novak

et al. 2015

Self Cite

We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the superconformal tensor calculus (formulated in the early 2000's) upon gauging away a number of superfluous fields. On the other hand, a different gauge fixing reduces our formulation to the SU(2) superspace of arXiv:0802.3953, which is suitable to describe the most general off-shell supergravity-matter couplings. Using the conformal superspace approach, we show how to reproduce practically all off-shell constructions derived so far, including the supersymmetric extensions of R 2 terms, thus demonstrating the power of our formulation. Furthermore, we construct for the first time a supersymmetric completion of the Ricci tensor squared term using the standard Weyl multiplet coupled to an off-shell vector multiplet. In addition, we present several procedures to generate higher-order off-shell invariants in supergravity, including higher-derivative ones. The covariant projective multiplets proposed in arXiv:0802.3953 are lifted to conformal superspace, and a manifestly superconformal action principle is given. We also introduce unconstrained prepotentials for the vector multiplet, the O(2) multiplet (i.e., the linear multiplet without central charge) and O(4 + n) multiplets, with n = 0, 1, . . . Superform formulations are given for the BF action and the non-abelian Chern-Simons action. Finally, we describe locally supersymmetric theories with gauged central charge in conformal superspace.