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Register a new userSuperspace Gauge Fixing in Yang-Mills Matter Coupled Conformal Supergravity
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In $D=4$, $cal{N}=1$ conformal superspace, the Yang-Mills matter coupled supergravity system is constructed where the Yang-Mills gauge interaction is introduced by extending the superconformal group to include the Kahler isometry group of chiral matter fields. There are two gauge-fixing procedures to get to the component Poincare supergravity: one via the superconformal component formalism and the other via the Poincare superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.
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The projective superspace formulation for four-dimensional N = 2 matter-coupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the N = 2 Weyl multiplet in which the structure group is SL(2,C) x SU(2) and the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howes realization of N = 2 conformal supergravity in which the tangent space group is SL(2,C) x U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the extension.
Using simple symmetry arguments we classify the ungauged $D=4$, $mathcal{N}=2$ supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of $mathcal{N}=2$ and $mathcal{N}=0$ matter-coupled Yang-Mills gauge theories. This includes all such supergravities with two isolated exceptions: pure supergravity and the $T^3$ model.
We find a formulation of $mathcal{N}=2$ supersymmetric Yang-Mills theory in Projective superspace. In particular we find an expression for the field strength in terms of an unconstrained prepotential which is desirable when quantizing the theory. We use this to write the action in terms of the prepotential and show that it reduces to the known result in the abelian limit.
Various gauge invariant but non-Yang-Mills dynamical models are discussed: Precis of Chern-Simons theory in (2+1)-dimensions and reduction to (1+1)-dimensional B-F theories; gauge theories for (1+1)-dimensional gravity-matter interactions; parity and gauge invariant mass term in (2+1)-dimensions.
We reconstruct the action of $N=1, D=4$ Wess-Zumino and $N=1, 2, D=4$ super-Yang-Mills theories, using integral top forms on the supermanifold ${cal M}^{(4|4)}$. Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.
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