Non-linear Realization Of Supersymmetry Research Articles

Constrained superfields in dynamical background

We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting derivative terms to obtain algebraic constraints on superfields. Thanks to the supersymmetry breaking contribution by the kinetic energy, the validity of constrained superfields can be extended to cosmological regimes and phenomena such as reheating after inflation, kinetic-energy domination, and the kinetic and standard misalignment of axion.

Identities in nonlinear realizations of supersymmetry

In this paper, we emphasize that a UV SUSY-breaking theory can be realized either linearly or nonlinearly. Both realizations form the dual descriptions of the UV SUSY-breaking theory. Guided by this observation, we find subtle identities involving the Goldstino field and matter fields in the standard nonlinear realization from trivial ones in the linear realization. Rather complicated integrands in the standard nonlinear realization are identified as total-divergences. Especially, identities only involving the Goldstino field reveal the self-consistency of the Grassmann algebra. As an application of these identities, we prove that the nonlinear Kahler potential without or with gauge interactions is unique, if the corresponding linear one is fixed. Our identities pick out the total-divergence terms and guarantee this uniqueness.

The Goldstino field in linear and nonlinear realizations of supersymmetry

A Goldstino field in the nonlinear realization of supersymmetry is constructed from an appropriate chiral super-multiplet of the linear theory, in general O'Raifeartaigh-like models. The linear theories can thus be reformulated into their nonlinear versions, via the standard procedure. The Goldstino field disappears totally from the original Lagrangian in the process, but reemerges in the Jacobian of the transformation and covariant derivatives. Vertices with Goldstino fields carry at least one space–time derivative, as one would have expected.

Constrained superfields and standard realization of nonlinear supersymmetry

A constrained superfield formalism has been proposed in [10] to analyze the low energy physics related to Goldstinos. We prove that this formalism can be reformulated in the language of standard realization of nonlinear supersymmetry. New relations have been uncovered in the standard realization of nonlinear supersymmetry.

Nonlinear realization of supersymmetry and superconformal symmetry

Nonlinear realizations describing the spontaneous breakdown of supersymmetry and $R$-symmetry are constructed using the Goldstino and $R$-axion fields. The associated $R$-current, supersymmetry current and energy-momentum tensor are shown to be related under the nonlinear supersymmetry transformations. Nonlinear realizations of the superconformal algebra carried by these degrees of freedom are also displayed. The divergences of the $R$ and dilatation currents are related to the divergence of the superconformal currents through nonlinear supersymmetry transformations which in turn relates the explicit breakings of these symmetries.

Non-linear realization of ℵ -extended supersymmetry

As generalizations of the original Volkov-Akulov action in four-dimensions, actions are found for all space-time dimensions D invariant under N non-linear realized global supersymmetries. We also give other such actions invariant under the global non-linear supersymmetry. As an interesting consequence, we find a non-linear supersymmetric Born-Infeld action for a non-Abelian gauge group for arbitrary D and N, which coincides with the linearly supersymmetric Born-Infeld action in D=10 at the lowest order. For the gauge group U({\cal N}) for M(atrix)-theory, this model has {\cal N}^2-extended non-linear supersymmetries, so that its large {\cal N} limit corresponds to the infinitely many (\aleph_0) supersymmetries. We also perform a duality transformation from F_{\mu\nu} into its Hodge dual N_{\mu_1...\mu_{D-2}}. We next point out that any Chern-Simons action for any (super)groups has the non-linear supersymmetry as a hidden symmetry. Subsequently, we present a superspace formulation for the component results. We further find that as long as superspace supergravity is consistent, this generalized Volkov-Akulov action can further accommodate such curved superspace backgrounds with local supersymmetry, as a super p-brane action with fermionic kappa-symmetry. We further elaborate these results to what we call `simplified' (Supersymmetry)^2-models, with both linear and non-linear representations of supersymmetries in superspace at the same time. Our result gives a proof that there is no restriction on D or N for global non-linear supersymmetry. We also see that the non-linear realization of supersymmetry in `curved' space-time can be interpreted as `non-perturbative' effect starting with the `flat' space-time.

Effective Lagrangians and light gravitino phenomenology

We construct the low-energy effective lagrangian for a light gravitino coupled to the minimal supersymmetric standard model under the assumption that supersymmetry breaking is communicated to the observable sector dominantly through soft terms. Our effective lagrangian is written in terms of the spin-1/2 Goldstino (the longitudinal component of the gravitino) transforming under a non-linear realization of supersymmetry. In this lagrangian, the Goldstino is derivatively coupled and all couplings of the Goldstino to light fields are determined uniquely by the supersymmetry-breaking scale \sqrt{F}. This lagrangian is therefore a useful starting point for further investigation of the light gravitino in gauge-mediated supersymmetry breaking models. We show that the invisible width of the Z into Goldstinos gives the constraint \sqrt{F} > 140 GeV.

Non-linear realizations of supersymmetry with off-shell central charges

We present a new class of non-linear realizations of the extended supersymmetry algebra with central charges. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as in the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. We work in two dimensions and discuss its extension to higher dimensions.

Non-linear realizations of supersymmetry with off-shell central charges

We present a new class of non-linear realizations of the extended supersymmetry algebra with central charges. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as in the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. We work in two dimensions and discuss its extension to higher dimensions.

The nonlinear realizations of the supersymmetry in the unconstrained curved superspace

The nonlinear realizations of supersymmetry are generalized to unconstrained curved superspace. To this aim an enlarged superspace\((z,\Theta ^\alpha ,\bar \Theta _{\dot \alpha } )\) in the same way as the flat superspace is defined; the coordinates of this enlarged superspace are not all independent, but it has two equivalent subspaces with independent coordinates: the subspace\(z = (x^m ,\theta ^\mu ,\bar \theta _{\dot \mu } )\) and the subspace\((x^m ,\Theta ^\alpha ,\bar \Theta _{\dot \alpha } )\).

Composite gravity and composite supergravity from non-linear realizations of supersymmetry

Using non-linear realizations of OSp( N;4), we define composite vierbeins ( N⩾1), composite SL(2, C) curvatures ( N⩾1) and composite achtbein superfields ( N⩾2). Composite gravity and composite supergravity models are proposed. We show that one can construct, from one set of fundamental Goldstone fields, the composite gravity as well as the composite Yang-Mills theory describing internal symmetries.

Non-linear realization of supersymmetry in anti de Sitter space

We derive the non-linear transformation law and the non-linear Lagrangian for a Goldstone spinor corresponding to spontaneous breaking of global supersymmetry in a de Sitter space with O(3,2) invariance (anti de Sitter space). With a suitable choice of the Goldstone spinor field the Lagrangian agrees with the form suggested by the coupling to supergravity. The construction is also valid for the case of extended supersymmetry.