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Abstract We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on Lorentzian manifolds and the Killing spinor equations that their supersymmetry parameters obey. This gives rise to a set of algebraic and differential Killing spinor equations that are obeyed by the supersymmetry parameters of the resulting three-dimensional non-relativistic field theories. We derive necessary and sufficient conditions that determine whether a Newton-Cartan background admits non-trivial solutions of these Killing spinor equations. Two classes of examples of Newton-Cartan backgrounds that obey these conditions are discussed. The first class is characterised by an integrable foliation, corresponding to so-called twistless torsional geometries, and includes manifolds whose spatial slices are isomorphic to the Poincaŕe disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds.

The notion of Q7branes and Qinstantons is introduced. These are onehalf BPS solutions of the type IIB supergravity theory characterized by a set of three parameters p,q,r such that r^2>4pq. The numbers p,q,r parameterize the electric and magnetic couplings of, respectively, the Q7branes and Qinstantons to a triplet of 8forms. The p,q 7branes and instantons including the D7brane and the Dinstanton have r2= 4pq. Sevenbrane solutions containing Q7branes are discussed and the Qinstanton onshell action is computed. The Q7branes are either novel bound states of a p,q 7brane and a p′,q′ 7brane with p,q ≠ p′,q′ or they form an independent new object in the theory. [ABSTRACT FROM AUTHOR]

In order to construct globally well-defined 7-brane solutions we postulate the existence of a new type of 7-brane. We show that these new 7-branes play an important role in understanding both the existing F-theory 7-brane configurations as well as more general 7-brane configurations. [ABSTRACT FROM AUTHOR]