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A bstract We construct the four-derivative supersymmetric extension of (1, 0), 6 D supergravity coupled to Yang-Mills and hypermultiplets. The hypermultiplet scalars are taken to parametrize the quaternionic projective space Hp ( n ) = Sp( n , 1)/Sp( n ) × Sp(1) R . The hyperscalar kinetic term is not deformed, and the quaternionic Kähler structure and symmetries of Hp ( n ) are preserved. The result is a three parameter Lagrangian supersymmetric up to first order in these parameters. Considering the case of Hp (1) we compare our result with that obtained from the compactification of 10 D heterotic supergravity on four-torus, consistently truncated to N = (1, 0), in which the hyperscalars parametrize SO(1, 4)/SO(4). We find that depending on how the Sp(1) is embedded in the SO(4), the results agree for a specific value of the parameter that governs the higher derivative hypermultiplet couplings. 

A bstract We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real form. A simple diagrammatic rule for solving the section constraint by inspection of the Satake diagram is derived. 

A bstract There exist two four-derivative extensions of N = (1, 0) supergravity in six dimensions. A particular combination of them is known to dualize to the analog of the Bergshoeff-de Roo (BdR) action in 10 D . Here we first show that the two extensions are not related to each other by any field redefinitions. Next, we dualize them separately thereby obtaining a two parameter dual theory. This is done directly at the level of the action, thus avoiding the laborious method of integrating equations of motion of the dualized theory into an action. To explore whether a similar phenomenon exists in 10 D , we study the dualization of the BdR action in 10 D in detail. We find an obstacle in the separation of the result into a sum of two independent invariants because of the presence of terms which do not lift from 6 D to 10 D . We also compare the dual of the BdR action with an existing result obtained in superspace. We find that the bosonic actions agree modulo field redefinitions. 

A bstract Higher derivative couplings of hypermultiplets to 6 D, N = (1 , 0) supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order α ′ higher derivative corrections. Reduction on T 4 is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset SO(4 , 4) / (SO(4) × SO(4)). While the SO(4 , 4) symmetry is ensured by Sen’s construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the SO(4) × SO(4) down to its SO(4) diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction. 

A bstract We construct a pseudo-Lagrangian that is invariant under rigid E 11 and transforms as a density under E 11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E 11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E 11 -representation together with the E 11 coset fields. We show that, in combination with gauge-invariant and E 11 -invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E 8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E 10 sigma model.