We derive the coupling of a hypermultiplet of N = 2 global supersymmetry to the Dirac-Born-Infeld Maxwell theory with linear N = 1 and a second nonlinear supersymmetry. At the level of global supersymmetry, this construction corresponds to the interaction with Maxwell brane fields of bulk hypermultiplets, such as the universal dilaton of type IIB strings compactified on a Calabi-Yau manifold. It displays in particular the active role of a four-form field. Constrained N = 1 and N = 2 superfields and the formulation of the hypermultiplet in its single-tensor version are used to derive the nonlinear realization, allowing a fully off-shell description. Exact results with explicit symmetries and supersymmetries are then obtained. The electric-magnetic dual version of the theory is also derived and the gauge structure of the interaction is exemplified with N = 2 nonlinear QED of a charged hypermultiplet. Its Higgs phase describes a novel super-Higgs mechanism without gravity, where the goldstino is combined with half of the hypermultiplet into an N = 1 massive vector multiplet.

The string coupling of N = 2 supersymmetric compactifications of type II string theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hypermultiplet, that has four real scalars living on a quaternion-Kähler manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of perturbative isometries, reduces the possible manifolds to a one-parameter family that describes the tree-level effective action deformed by the only possible perturbative correction arising at one-loop level. A similar argument can be made at the level of global supersymmetry where the scalar manifold is hyper-Kähler. In this work, the connection between global and local supersymmetry is explicitly constructed, providing a non-trivial gravity decoupled limit of type II strings already in perturbation theory.

Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N = 1 super-Yang-Mills theory fully compatible with the expected all-order behaviour or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ β function from algebraic arguments only. The extension of results to N = 2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16 B + 16 F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1) R currents. As a byproduct, we show under which conditions the S multiplet can be improved to contain the Callan-Coleman-Jackiw energy-momentum tensor whose trace measures the breaking of scale invariance.