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Register a new userUnified non-metric (1,0) tensor-Einstein supergravity theories and (4,0) supergravity in six dimensions
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Murat Gunaydin
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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 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 $d=6$.
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Sergei M. Kuzenko
, Ulf Lindstrom
, Emmanouil S. N. Raptakis andn Gabriele Tartaglino-Mazzucchelli
2020
General $mathcal{N}=(1,0)$ supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) $mathsf{SU}(2)$ superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield $epsilon^alpha$, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector $xi^a$ and tensor $zeta^{a(n)}$ superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal dAlembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on conformally flat backgrounds.
We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local symmetry group that is (i) simple, and (ii) acts irreducibly on all the vector fields of the theory, including the ``graviphoton. Restricting ourselves to the theories that originate from five dimensions via dimensional reduction, we find that the generic Jordan family of MESGTs with the scalar manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four dimensions with the unifying global symmetry group SO(2,n). Of these theories only one can be gauged so as to obtain a unified YMESGT with the gauge group SO(2,1). Three of the four magical supergravity theories defined by simple Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions. Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family and the theories whose scalar manifolds are homogeneous but not symmetric do not lead to unified MESGTs in four dimensions. The three infinite families of unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras, whose scalar manifolds are non-homogeneous, do not lead directly to unified MESGTs in four dimensions under dimensional reduction. However, since their manifolds are non-homogeneous we are not able to completely rule out the existence of symplectic sections in which these theories become unified in four dimensions.
The supersymmetrization of curvature squared terms is important in the study of the low-energy limit of compactified superstrings where a distinguished role is played by the Gauss-Bonnet combination, which is ghost-free. In this letter, we construct its off-shell ${cal N} = (1, 0)$ supersymmetrization in six dimensions for the first time. By studying this invariant together with the supersymmetric Einstein-Hilbert term we confirm and extend known results of the $alpha$-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the ${rm AdS}_3times{rm S}^3$ solution.
We describe the supersymmetric completion of several curvature-squared invariants for ${cal N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the case of minimal off-shell Poincare supergravity based on the dilaton-Weyl multiplet coupled to a linear multiplet as a conformal compensator, we describe off-shell supersymmetric completions for all the three possible purely gravitational curvature-squared terms in six dimensions: Riemann, Ricci, and scalar curvature squared. A linear combination of these invariants describes the off-shell completion of the Gauss-Bonnet term, recently presented in arXiv:1706.09330. We study properties of the Einstein-Gauss-Bonnet supergravity, which plays a central role in the effective low-energy description of $alpha^prime$-corrected string theory compactified to six dimensions, including a detailed analysis of the spectrum about the ${rm AdS}_3times {rm S}^3$ solution. We also present a novel locally superconformal invariant based on a higher-derivative action for the linear multiplet. This invariant, which includes gravitational curvature-squared terms, can be defined both coupled to the standard-Weyl or dilaton-Weyl multiplet for conformal supergravity. In the first case, we show how the addition of this invariant to the supersymmetric Einstein-Hilbert term leads to a dynamically generated cosmological constant and non-supersymmetric (A)dS$_6$ solutions. In the dilaton-Weyl multiplet, the new off-shell invariant includes Ricci and scalar curvature-squared terms and possesses a nontrivial dependence on the dilaton field.
We construct N=1 supersymmetrisations of some recently-proposed theories of critical gravity, conformal gravity, and extensions of critical gravity in four dimensions. The total action consists of the sum of three separately off-shell supersymmetric actions containing Einstein gravity, a cosmological term and the square of the Weyl tensor. For generic choices of the coefficients for these terms, the excitations of the resulting theory around an AdS_4 background describe massive spin-2 and massless spin-2 modes coming from the metric; massive spin-1 modes coming from a vector field in the theory; and massless and massive spin-3/2 modes (with two unequal masses) coming from the gravitino. These assemble into a massless and a massive N=1 spin-2 multiplet. In critical supergravity, the coefficients are tuned so that the spin-2 mode in the massive multiplet becomes massless. In the supersymmetrised extensions of critical gravity, the coefficients are chosen so that the massive modes lie in a window of lowest energies E_0 such that these ghostlike fields can be truncated by imposing appropriate boundary conditions at infinity, thus leaving just positive-norm massless supergravity modes.
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