Superconformal Symmetry in Four Dimensions

We investigate the nonlinear realization of spontaneously broken N = 2 superconformal symmetry in 4 dimensions. We particularly study NambuGoldstone degrees of freedom for the partial breaking of N = 2 superconformal symmetry down to N = 1 super-Poincaré symmetry, where we get the chiral NG multiplet of dilaton and the vector NG multiplet of NG fermion of broken Q-supersymmetry. Evaluating the covariant differentials and supervielbeins for the chiral as well as the full superspace, we obtain the nonlinear effective lagrangians. KUCP-108 July 1997 ∗Supported in part by the Monbusho Grant-in-Aid for Scientific Research No. C-09640345 and for Scientific Research on Priority Areas No. 09246215 In the last few years there has been much interest in N = 2 supersymmetric gauge theory in the context of duality which provides us with the understanding of nonperturbative properties of supersymmetric field theories as well as string theories. Hughes, Liu and Polchinski [1] pointed out that N = 2 global supersymmetry can be partially broken down to N = 1 supersymmetry by giving the argument on the way how to evade the existing no-go theorem of partial breaking of extended supersymmetry based on the supersymmetry current algebra. They also explicitly constructed the four-dimensional supermembrane solution of the six-dimensional supersymmetric gauge theory, in which the second supersymmetry, in the equivalent four-dimensional N = 2 theory, is spontaneously broken and the partial breaking is realized. While, Antoniadis, Partouche and Taylor [2] introduced the electric and magnetic Fayet-Iliopoulos terms in the N = 2 gauge theory of abelian vector multiplet and have shown that there occurs spontaneous breaking of N = 2 to N = 1 supersymmetry. This partial breaking induced by the Fayet-Iliopoulos terms has also been obtained by taking the flat limit of the N = 2 supergravity theories [3]. Bagger and Galperin [4, 5] have studied the nonlinear realization of N = 2 supersymmetry partially broken down to N = 1 supersymmetry [6, 7] and obtained the Nambu-Goldstone multiplet both for the cases; chiral multiplet [4] and vector-multiplet [5], and discussed the nonlinear transformation laws as well as the low-energy effective lagrangians [8]. Here in this paper, we shall investigate the nonlinear realization of N = 2 extended superconformal symmetry in four-dimensions, which is realized for the case of vanishing β-function in the N=2 supersymmetric QCD. We study the spontaneously breaking of this symmetry down to N = 1 super-Poincaré symmetry. We identify the NambuGoldstone degrees of freedom corresponding to the broken charges. It turns out that there appear a vector multiplet of NG fermion of the broken second Q-supersymmetry as well as a chiral multiplet of dilaton, axion and dilatino which are associated with the broken dilatation, chiral U(1) rotation and the first S-supersymmetry generators. We note that the NG fermion of the broken second S-supersymmetry can be expressed as the derivative of the true NG-fermion of the second Q-supersymmetry. We obtain the effective interaction for the system of the dilaton multiplet coupled to the NG-vector