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Register a new userNonlinear Realization of N=2 Superconformal Symmetry and Brane Effective Actions
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Lu-Xin Liu
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Due to the incompatibility of the nonlinear realization of superconformal symmetry and dilatation symmetry with the dilaton as the compensator field, in the present paper it shows an alternative mechanism of spontaneous breaking the N=2 superconformal symmetry to the N=0 case. By using the approach of nonlinear transformations it is found that it leads to a space-filling brane theory with Weyl scale W(1,3) symmetry. The dynamics of the resulting Weyl scale invariant brane, along with that of other Nambu-Goldstone fields, is derived in terms of the building blocks of the vierbein and the covariant derivative from the Maurer-Cartan oneforms. A general coupling of the matter fields localized on the brane world volume to these NG fields is also constructed.
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Nonlinear supersymmetry is used to compute the general form of the effective D-brane action in type I string theory compactified to four dimensions in the presence of internal magnetic fields. In particular, the scalar potential receives three contributions: (1) a nonlinear part of the D-auxiliary component, associated to the Dirac-Born-Infeld action; (2) a Fayet-Iliopoulos (FI) D-term with a moduli-dependent coefficient; (3) a D-auxiliary independent (but moduli dependent) piece from the D-brane tension. Minimization of this potential leads to three general classes of vacua with moduli stabilization: (i) supersymmetric vacua allowing in general FI terms to be cancelled by non-trivial vacuum expectation values (VEVs) of charged scalar fields; (ii) anti-de Sitter vacua of broken supersymmetry in the presence of a non-critical dilaton potential that can be tuned at arbitrarily weak string coupling; (iii) if the dilaton is fixed in a supersymmetric way by three-form fluxes and in the absence of charged scalar VEVs, one obtains non supersymmetric vacua with positive vacuum energy.
The action of Weyl scale invariant p=2 brane which breaks the target super Weyl scale symmetry in the N=1, D=4 superspace down to the lower dimensional Weyl symmetry W(1,2) is derived by the approach of nonlinear realization. The dual form action for the Weyl scale invariant supersymmetric D2 brane is also constructed. The interactions of localized matter fields on the brane with the Nambu-Goldstone fields associated with the breaking of the symmetries in the superspace and one spatial translation directions are obtained through the Cartan one-forms of the Coset structures. The covariant derivatives for the localized matter fields are also obtained by introducing Weyl gauge field as the compensating field corresponding to the local scale transformation on the brane world volume.
We explore a nonlinear realization of the (2+1)-dimensional Lorentz symmetry with a constant vacuum expectation value of the second rank anti-symmetric tensor field. By means of the nonlinear realization, we obtain the low-energy effective action of the Nambu-Goldstone bosons for the spontaneous Lorentz symmetry breaking.
N=1, d=4 superconformal group is studied and its representations are discussed. Under superconformal transformations, left invariant derivatives and some class of superfields, including supercurrents, are shown to follow these representations. In other words, these superfields are quasi-primary by analogy with two dimensional conformal field theory. Based on these results, we find the general forms of the two-point and the three-point correlation functions of the quasi-primary superfields in a group theoretical way. In particular, we show that the two-point function of the supercurrent is unique up to a constant and the general form of the three-point function of the supercurrent has two free parameters.
We demonstrate that all rational models of the N=2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhus algebra (for which we give a physically motivated derivation) explicitly for certain theories, we analyse the modular properties of some of the vacuum characters, and we use the coset realisation of the algebra in terms of su_2 and two free fermions. Some of our arguments generalise to the Kazama-Suzuki models indicating that all rational N=2 supersymmetric models might be unitary.
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