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We elaborate on the duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is presented by a function E depending on the auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics models admit a simple off-shell characterization in terms of this function. In the standard formulation, the continuous U (1) duality symmetry is nonlinearly realized on the Maxwell field strength. In the new setting, the same symmetry acts as linear U (1) transformations of the auxiliary field variables. The nonlinear U (1) duality condition proves to be equivalent to the linear U (1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. For a class of duality-symmetric Lagrangians we introduce an alternative representation with the auxiliary scalar field and find new explicit examples of such systems.1 A preliminary version of this approach was presented in [8,9].

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We show that any conformal field theory in d-dimensional Minkowski space, in a phase with spontaneously broken conformal symmetry and with the dilaton among its fields, can be rewritten in terms of the static gauge (d − 1)-brane on AdS (d+1) by means of an invertible change of variables. This nonlinear holographic transformation maps the Minkowski space coordinates onto the brane worldvolume ones and the dilaton onto the transverse AdS brane coordinate. One of the consequences of the existence of this map is that any (d − 1)-brane worldvolume action on AdS (d+1) × X m (with X m standing for the sphere S m or more complicated curved manifold) admits an equivalent description in Minkowski space as a nonlinear and higher-derivative extension of some conventional conformal field theory action, with the conformal group being realized in a standard way. The holographic transformation explicitly relates the standard realization of the conformal group to its field-dependent nonlinear realization as the isometry group of the brane AdS (d+1) background. Some possible implications of this transformation, in particular, for the study of the quantum effective action of N = 4 super Yang-Mills theory in the context of AdS/CFT correspondence, are briefly discussed. * bellucci@lnf.infn.it †