$$ \mathcal{N} $$ = 2 supersymmetric partially massless fields and other exotic non-unitary superconformal representations

We find and classify the simplest $$ \mathcal{N} $$ N = 2 SUSY multiplets on AdS4 which contain partially massless fields. We do this by studying representations of the $$ \mathcal{N} $$ N = 2, d = 3 superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the $$ \mathcal{N} $$ N = 1 case, the simplest $$ \mathcal{N} $$ N = 2 multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that $$ \mathcal{N} $$ N = 2 supersymmetry allows for short multiplets that contain partially massless spin-s particles of depth t = s − 2.

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

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.

Harish-Chandra Modules of the Intermediate Series over the Topological N = 2 Superconformal Algebra

The topological N = 2 superconformal algebra was introduced by Dijkgraaf, Verlinde and Verlinde as the symmetry algebra of topological strings at d < 1. We give a classification of irreducible 𝕫 × 𝕫-graded modules of the intermediate series over this infinite-dimensional Lie superalgebra.

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-$$BMS_3$$BMS3, the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the $$\mathfrak {so}(2,2)\oplus \mathfrak {so}(2,1)$$so(2,2)⊕so(2,1) gravity theories. We extend our results to the $$\mathcal {N}=2$$N=2 and $$\mathcal {N}=4$$N=4 cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit $$\ell \rightarrow \infty $$ℓ→∞.

Super-biderivations and linear super-commuting maps on the twisted N = 2 superconformal algebra

In this paper, we will first determine all the super-skewsymmetric super-biderivations of the twisted [Formula: see text] superconformal algebra [Formula: see text], and prove that every super-skewsymmetric super-biderivation of the twisted [Formula: see text] superconformal algebra [Formula: see text] is inner. Then, we will show that all the linear super-commuting maps on the twisted [Formula: see text] superconformal algebra [Formula: see text] are standard.