Abstract
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.
Highlights
It is notorious that N = 2 supersymmetry, global or local, forbids a dependence on hypermultiplet scalars of gauge kinetic terms
In N = 2 supergravity, the scalar manifold is the product of a quaternion-Kahler (Einstein) manifold, for hypermultiplet scalars [1], and a Kahler manifold of a special type for vector multiplet scalars [2]
In global N = 2 supersymmetry, the quaternion-Kahler manifold of hypermultiplet scalars is replaced by a Ricci-flat hyperkahler space [3]
Summary
If we consider a theory with a broken, nonlinear supersymmetry realized in a goldstino mode, another unbroken linear supersymmetry and a DBI super-Maxwell system coupled to hypermultiplet fields, we certainly expect that the allowed Lagrangians are severely restricted. Analyzing these restrictions is the main motivation of this paper. Our first objective is to describe, in the context of linear N = 2 supersymmetry, the coupling of the single-tensor multiplet to N = 2 super-Maxwell theory Since these two supermultiplets admit off-shell realizations, they can be described in superspace without reference to a particular Lagrangian. Gauge transformations of the Maxwell multiplet use a single-tensor multiplet, we begin with the latter
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