Abstract
We investigate exotic supergravity theories in 6D with maximal (4,0) and (3,1) supersymmetry, which were conjectured by C. Hull to exist and to describe strong coupling limits of ${\cal N}=8$ theories in 5D. These theories involve exotic gauge fields with non-standard Young tableaux representations, subject to (self-)duality constraints. We give novel actions in a 5+1 split of coordinates whose field equations reproduce those of the free bosonic (4,0) and (3,1) theory, respectively, including the (self-)duality relations. Evidence is presented for a master exceptional field theory formulation with an extended section constraint that, depending on the solution, produces the (4,0), (3,1) or the conventional (2,2) theory. We comment on the possible construction of a fully non-linear master exceptional field theory.
Highlights
Among the surprising features of string/M-theory is the possible existence of exotic superconformal field and gravity theories in six dimensions, which display generalizations of electric-magnetic duality
In this paper our focus will be on a conjecture by Hull [1,2] according to which there are strong coupling limits of N 1⁄4 8 theories in five dimensions that are given by six-dimensional theories with chiral N 1⁄4 ð4; 0Þ and N 1⁄4 ð3; 1Þ supersymmetry, respectively
As one of the most enticing outcomes of our investigation we find evidence for a master exceptional field theory formulation in which the conventional N 1⁄4 ð2; 2Þ theory as well as the N 1⁄4 ð4; 0Þ and N 1⁄4 ð3; 1Þ theory are obtained through different solutions of an extended section constraint of the form dMN K ∂ N
Summary
Among the surprising features of string/M-theory is the possible existence of exotic superconformal field and gravity theories in six dimensions, which display generalizations of electric-magnetic duality. In this paper our focus will be on a conjecture by Hull [1,2] according to which there are strong coupling limits of N 1⁄4 8 theories in five dimensions that are given by six-dimensional theories with chiral N 1⁄4 ð4; 0Þ and N 1⁄4 ð3; 1Þ supersymmetry, respectively Such theories must be exotic or nongeometric since they feature mixed symmetry tensors of Young tableaux type and , respectively, instead of a conventional graviton, suggesting the need for a generalized notion of spacetime and diffeomorphism invariance. In this paper we will present actions for (the bosonic sectors of) the free exotic 6D theories that generalize the (linearized) E6ð6Þ exceptional field theory [10,11] by adding one more “exotic” coordinate to the 27, as suggested by the singlet central charge in (1.1).
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