We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a nonrelativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces, and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension $D=d+1$ (no central charges), as well as in the special dimension $D=2+1$ with one exotic central charge. We obtain new classical mechanics models which extend the standard ($D=0+1$) conformal mechanics in the presence of $d$ nonvanishing space dimensions. DOI: http://dx.doi.org/10.1103/PhysRevD.83.085013 © 2011 American Physical Society

We present, for the first time, the complete off-shell 4D, $$ \mathcal{N} $$N = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the $$ \mathcal{N} $$N = 2 harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{++} $$h α s − 1 α ̇ s − 1 + + , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-2\right)}^{++} $$h α s − 2 α ̇ s − 2 + + and two conjugated complex analytic spinor superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{+3} $$h α s − 1 α ̇ s − 1 + 3 , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-1\right)}^{+3} $$h α s − 2 α ̇ s − 1 + 3 , where α(s) := (α₁. . . α_s), $$ \dot{\alpha} $$α ̇ (s) := ( $$ \dot{\alpha} $$α ̇ ₁. . . $$ \dot{\alpha} $$α ̇ _s). Like in the harmonic superspace formulations of $$ \mathcal{N} $$N = 2 Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content (s,s−1/2,s−1/2,s−1) is restored. For s = 2 the action describes the linearized version of “minimal” $$ \mathcal{N} $$N = 2 Einstein supergravity.

We revisit the issue of higher-dimensional counterterms for the \( \mathcal{N}=\left(1,1\right) \) supersymmetric Yang-Mills (SYM) theory in six dimensions using the off-shell \( \mathcal{N}=\left(1,0\right) \) and on-shell \( \mathcal{N}=\left(1,1\right) \) harmonic superspace approaches. The second approach is developed in full generality and used to solve, for the first time, the \( \mathcal{N}=\left(1,1\right) \) SYM constraints in terms of \( \mathcal{N}=\left(1,0\right) \) superfields. This provides a convenient tool to write explicit expressions for the candidate counterterms and other \( \mathcal{N}=\left(1,1\right) \) invariants and may be conducive to proving non-renormalization theorems needed to explain the absence of certain logarithmic divergences in higher-loop contributions to scattering amplitudes in \( \mathcal{N}=\left(1,1\right) \) SYM.

Motivated by recent progress in studying the duality-symmetric models of nonlinear electrodynamics, we revert to the auxiliary tensorial (bispinor) field formulation of the $O(2)$ duality proposed by us in Ivanov and Zupnik [Nucl. Phys. B618, 3 (2001); Yad. Fiz. 67, 2212 (2004)]. In this approach, the entire information about the given duality-symmetric system is encoded in the $O(2)$-invariant interaction Lagrangian which is a function of the auxiliary fields ${V}_{$\alpha${}$\beta${}}$, ${\overline{V}}_{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{$\alpha${}}\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{$\beta${}}}$. We extend this setting to duality-symmetric systems with higher derivatives and show that the recently employed ``nonlinear twisted self-duality constraints'' amount to the equations of motion for the auxiliary tensorial fields in our approach. Some other related issues are briefly discussed and a few instructive examples are explicitly worked out.

We develop a new superfield approach to $\mathcal{N}=4$ supersymmetric mechanics based on the concept of biharmonic superspace (bi-HSS). It is an extension of the $\mathcal{N}=4$, $d=1$ superspace by two sets of harmonic variables associated with the two SU(2) factors of the $R$-symmetry group SO(4) of the $\mathcal{N}=4$, $d=1$ super Poincaré algebra. There are three analytic subspaces in it: two of the Grassmann dimension 2 and one of the dimension 3. They are closed under the infinite-dimensional “large” $\mathcal{N}=4$ superconformal group, as well as under the finite-dimensional superconformal group $D(2,1;\alpha )$. The main advantage of the bi-HSS approach is that it gives an opportunity to treat $\mathcal{N}=4$ supermultiplets with finite numbers of off-shell components on equal footing with their “mirror” counterparts. We show how such multiplets and their superconformal properties are described in this approach. We also define nonpropagating gauge multiplets which can be used to gauge various isometries of the bi-HSS actions. We present an example of a nontrivial $\mathcal{N}=4$ mechanics model with a seven-dimensional target manifold obtained by gauging a U(1) isometry in a sum of the free actions of the multiplet $(\mathbf{4},\mathbf{4},\mathbf{0})$ and its mirror counterpart.