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After the Weyl multiplet is introduced, we can now define matter multiplets whose transformations respect the algebra with structure functions that depend on the fields of the Weyl multiplet. We treat here vector multiplets and hypermultiplets. We define them for D = 4, 5 and 6, first for rigid supersymmetry and then for the superconformal theory. In the second part of this chapter we define actions for these multiplets, which will be the basis for the further chapters. [ABSTRACT FROM AUTHOR]

In this chapter, we will discuss the gauge multiplets of the superconformal algebra, called Weyl multiplets. We start by repeating the basic transformation rules for gauge fields and curvatures, and discuss then the modifications necessary for spacetime symmetries. We will see that one needs constraints on curvatures, and will learn how to deal with them. At the end of this chapter we obtain a Weyl multiplets for N = 2 theories in D = 4, D = 5 and D = 6. [ABSTRACT FROM AUTHOR]

The previous part of this book first considered conformal couplings, and finally these were projected to a subspace after gauge choices. We saw how then special and quaternionic-Kähler geometries emerge. In this chapter we obtain the final action and transformation laws for N = 2, D = 4 (Sect. 6.1) and D = 5 (Sect. 6.2) Poincaré supergravity coupled to nV vector multiplets and nH hypermultiplets after elimination of auxiliary fields and in terms of the variables of Poincaré supergravity. We end with final remarks indicating also future directions. [ABSTRACT FROM AUTHOR]

In this chapter we will discuss the geometric concepts behind the special geometries. In terms of the supergravity theories, this means that we will restrict to the bosonic sector of these theories. In the first part of this chapter, we will examine the scalars of the vector multiplets, and we will see that the special Kähler geometry for the scalars is very much related to the symplectic transformations defined by the dualities of the vector fields. We will also discuss the attractor mechanism for black holes in this context. Then we will study the geometry of quaternionic- Kähler manifolds, related to the scalars of the hypermultiplets. Finally, we will present the relations between these manifolds and their versions in the different dimensions. [ABSTRACT FROM AUTHOR]

In this chapter we combine the actions for vector multiplets and hypermultiplets, containing also compensating multiplets. We gauge fix the superconformal symmetries that are not necessary for the super-Poincaré theory, and in such way obtain matter-coupled Poincaré supergravity theories. We extensively discuss pure supergravity (using also other compensating multiplets leading to the off-shell theory) and discuss its reduction to N = 1. Then we discuss appropriate variables for the gauge fixing of general matter couplings. [ABSTRACT FROM AUTHOR]

We give an introduction to the book, discussing the role of the N = 2 theories, its geometric structure, and the superconformal tensor calculus. We also refer to other treatments. We then set out the plan of the book. In the second part of the chapter we introduce tools that are useful for the construction of superconformal gauge theory and multiplets. We first discuss the catalogue of supersymmetric theories with 8 supercharges (Sect. 1.2) and their multiplets (Sect. 1.2.1). After a short Sect. 1.2.2 with the strategy, we discuss the conformal (Sect. 1.2.3) and then superconformal (Sect. 1.2.4) groups. The transformations of the fields under the conformal symmetry are also given in Sect. 1.2.3, while for the fermionic symmetries, this is discussed in a short Sect. 1.2.5. [ABSTRACT FROM AUTHOR]

Defect Conformal Field Theories describe critical points of Quantum Field Theories excited or modified in the neighbourhood of a large p-dimensional submanifold. We elucidate the constraints of conformal invariance on correlation functions and we provide both recurrence relations, and in some cases exact results, for the conformal blocks with scalar external operators. [ABSTRACT FROM AUTHOR]