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Register a new userEffective Action of the N = 2 Maxwell Multiplet in Harmonic Superspace
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We present, in the N=2, D=4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N=2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N=2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N=2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U(1)-factor in the N=2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic corrections arise at leading order. These holomorphic contribution are consistent with Seibergs quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N=2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.
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The background field method for N=2 super Yang-Mills theories in harmonic superspace is developed. The ghost structure of the theory is investigated. It is shown that the ghosts include two fermionic real omega-hypermultiplets (Faddeev-Popov ghosts) and one bosonic real omega-hypermultiplet (Nielsen-Kallosh ghost), all in the adjoint representation of the gauge group. The one-loop effective action is analysed in detail and it is found that its structure is determined only by the ghost corrections in the pure super Yang-Mills theory. As applied to the case of N=4 super Yang-Mills theory, realized in terms of N=2 superfields, the latter result leads to the remarkable conclusion that the one-loop effective action of the theory does not contain quantum corrections depending on the N=2 gauge superfield only. We show that the leading low-energy contribution to the one-loop effective action in the N=2 SU(2) super Yang-Mills theory coincides with Seibergs perturbative holomorphic effective action.
We discuss possible actions for the d=2, N=(2,2) large vector multiplet that gauges isometries of generalized Kahler geometries. We explore two scenarios that allow us to write kinetic and superpotential terms for the scalar field-strengths, and write kinetic terms for the spinor invariants that can introduce topological terms for the connections.
We explicitly demonstrate that the perturbative holomorphic contribution to the off-shell effective action of N=2 U(1) gauge supermultiplet is an entire effect of the minimal coupling to a hypermultiplet with the mass generated by a central charge in N=2 superalgebra. The central charge is induced by a constant vacuum N=2 gauge superfield strength spontaneously breaking the automorphism U(1)_R symmetry of N=2 superalgebra. We use the manifestly off-shell supersymmetric harmonic superspace techniques of quantum calculations with the central charge-massive hypermultiplet propagator.
This paper presents a projective superspace formulation for 4D N = 2 matter-coupled supergravity. We first describe a variant superspace realization for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by the choice of the structure group (SO(3,1) x SU(2) versus SO(3,1) x U(2)), which implies that the super-Weyl transformations are generated by a covariantly chiral parameter instead of a real unconstrained one. We introduce various off-shell supermultiplets which are curved superspace analogues of the superconformal projective multiplets in global supersymmetry and which describe matter fields coupled to supergravity. A manifestly locally supersymmetric and super-Weyl invariant action principle is given. Off-shell locally supersymmetric nonlinear sigma models are presented in this new superspace.
Building on the superspace formulation for four-dimensional N=2 matter-coupled supergravity developed in arXiv:0805.4683, we elaborate upon a general setting for field theory in N=2 conformally flat superspaces, and concentrate specifically on the case of anti-de Sitter (AdS) superspace. We demonstrate, in particular, that associated with the N=2 AdS supergeometry is a unique vector multiplet such that the corresponding covariantly chiral field strength W_0 is constant, W_0=1. This multiplet proves to be intrinsic in the sense that it encodes all the information about the N=2 AdS supergeometry in a conformally flat frame. Moreover, it emerges as a building block in the construction of various supersymmetric actions. Such a vector multiplet, which can be identified with one of the two compensators of N=2 supergravity, also naturally occurs for arbitrary conformally flat superspaces. An explicit superspace reduction N=2 to N=1 is performed for the action principle in general conformally flat N=2 backgrounds, and examples of such reduction are given.
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