$$ \mathcal{N} $$ = 4 conformal supergravity: the complete actions

For every conformal gauge field h α(n)α(m) in four dimensions, with n ≥ m > 0, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) n = m = 1 (Maxwell's field) on arbitrary gravitational backgrounds; and (ii) n = m + 1 = 2 (conformal gravitino) and n = m = 2 (conformal graviton) on Bach-flat backgrounds. It is believed that in other cases certain lower-spin fields must be introduced to ensure gauge invariance in Bach-flat backgrounds, although no closedform model has yet been constructed (except for conformal maximal depth fields with spin s = 5/2 and s = 3). In this paper we derive such a gauge-invariant model describing the dynamics of a conformal gauge field h α(3)α coupled to a self-dual two-form. Similar to other conformal higher-spin theories, it can be embedded in an off-shell superconformal gaugeinvariant action. To this end, we introduce a new family of N = 1 superconformal gauge multiplets described by unconstrained prepotentials Υ α(n) , with n > 0, and propose the corresponding gauge-invariant actions on conformally-flat backgrounds. We demonstrate that the n = 2 model, which contains h α(3)α at the component level, can be lifted to a Bach-flat background provided Υ α(2) is coupled to a chiral spinor Ω α. We also propose families of (super)conformal higher-derivative non-gauge actions and new superconformal operators in any curved space. Finally, through considerations based on supersymmetry, we argue that the conformal spin-3 field should always be accompanied by a conformal spin-2 field in order to ensure gauge invariance in a Bach-flat background.

Section: Jhep08(2020)068mentioning

confidence: 99%

New locally (super)conformal gauge models in Bach-flat backgrounds

Kuzenko

Ponds

Raptakis

2020

“…In this section we will revisit the arguments made in [26] to show that the constraints coming from the higher Bianchi will follow from the preliminary constraints (2.22, 2.29). The argument is based on taking a Bianchi identity of the Bianchi identity.…”

Section: Bianchi Identity Of the Bianchi Identity: Constraints Frommentioning

confidence: 99%

“…This is a standard method which is used to construct invariant actions in supergravity in various dimensions (See [20][21][22][23]). It was first introduced in superspace as the 'ectoplasm principle' [24,25] and has been recently applied in [26] to construct the most general actions for N = 4 conformal supergravity. Similar ideas have also been used in rheonomic approach to supergravity [27,28].…”

Section: Introductionmentioning

confidence: 99%

New higher derivative action for tensor multiplet in $$ \mathcal{N} $$ = 2 conformal supergravity in four dimensions

Hegde

Sahoo

2020

Self Cite

We will use the covariant superform approach to develop a new density formula for N = 2 conformal supergravity which is based on a fermionic multiplet whose lowest component is a dimension-5/2 spinor. We will show that this density formula admits an embedding of the real scalar multiplet of [1]. Upon using the embedding of the tensor multiplet into the real scalar multiplet, we will construct a new higher derivative action of the tensor multiplet in N = 2 conformal supergravity.

“…12 The standard conformal supergravity theories in d = 4 based on the conformal superalgebras SU(2, 2|N ) exist only for N ≤ 4. All N =4 conformal supergravities in d = 4 have recently been constructed in [51,52]. In addition to a massless graviton they contain a massive spin two ghost field and hence are not unitary.…”

Section: Jhep06(2021)081mentioning

confidence: 99%

Unified non-metric (1, 0) tensor-Einstein supergravity theories and (4, 0) supergravity in six dimensions

Günaydın

2021

The ultrashort unitary (4, 0) supermultiplet of 6d superconformal algebra OSp(8∗|8) reduces to the CPT-self conjugate supermultiplet of 4d superconformal algebra SU(2, 2|8) that represents the fields of maximal N = 8 supergravity. The graviton in the (4, 0) multiplet is described by a mixed tensor gauge field which can not be identified with the standard metric in 6d. Furthermore the (4, 0) supermultiplet can be obtained as a double copy of (2, 0) conformal supermultiplet whose interacting theories are non-Lagrangian. It had been suggested that an interacting non-metric (4, 0) supergravity theory might describe the strongly coupled phase of 5d maximal supergravity. In this paper we study the implications of the existence of an interacting non-metric (4, 0) supergravity in 6d. The (4, 0) theory can be truncated to non-metric (1, 0) supergravity coupled to 5,8 and 14 self-dual tensor multiplets that reduce to three of the unified magical supergravity theories in d = 5. This implies that the three infinite families of unified N = 2, 5d Maxwell-Einstein supergravity theories (MESGTs) plus two sporadic ones must have uplifts to unified non-metric (1, 0) tensor Einstein supergravity theories (TESGT) in d = 6. These theories have non-compact global symmetry groups under which all the self-dual tensor fields including the gravitensor transform irreducibly. Four of these theories are uplifts of the magical supergravity theories whose scalar manifolds are symmetric spaces. The scalar manifolds of the other unified theories are not homogeneous spaces. We also discuss the exceptional field theoretic formulations of non-metric unified (1, 0) tensor-Einstein supergravity theories and conclude with speculations concerning the existence of higher dimensional non-metric supergravity theories that reduce to the (4, 0) theory in d = 6.