S. Krivonos

N = 4, d = 1 supermultiplets from nonlinear realizations of D(2, 1; α)

Proceeding from nonlinear realizations of the most general N = 4, d = 1 superconformal symmetry associated with the supergroup D(2, 1; ?), we construct all known and two new off-shell N = 4, d = 1 supermultiplets as properly constrained N = 4 superfields. We find plenty of nonlinear interrelations between the multiplets constructed and present a few examples of invariant superfield actions for them. The superconformal transformation properties of these multiplets are explicit within our method.

Geometric superfield approach to superconformal mechanics

The new general geometric approach to d=1 conformally invariant systems, previously elaborated by the authors with an example of conformal mechanics, is applied in the supersymmetry case. The authors construct a manifestly invariant superfield description of the superconformal mechanics (SCM) models for arbitrary even N, N being a number of independent real d=1 Poincare supersymmetries. These systems are shown to result from nonlinear realisations of d=1 superconformal groups SU(1,1 mod N/2) in the cosets SU(1,1 mod N/2)/U(N/2). For the N=4 case, which has previously been worked out only on shell, they find two different off-shell formulations related via a duality transformation. The systems with higher N are essentially new. An effect of creating the U(1) central charge in the d=1, N=4 superconformal algebra su(1,1 mod 2) by the duality transformation is revealed. By extending the procedure employed in the bosonic case they derive general superfield solutions of the N=2 and N=4 SCM equations.

A new class of superconformal sigma models with the Wess-Zumino action

Abstract We construct nonlinear sigma models for infinite-dimensional N -extended D = 2 superconformal symmetries (of the type ( N , N )). These are classically integrable and naturally incorporate the conformally invariant bosonic Wess-Zumino sigma model defined on the supersymmetry automorphism group SO − ( N ) × SO + ( N ). Their bosonic manifolds involve also the D = 2 dilaton and, in general, a number of additional fields. For the dilaton, both the free and Liouville actions are admissible (in the latter case - supplemented with proper Yukawa couplings), so the proposed models simultaneously provide higher- N superextensions of the D = 2 Liouville theory. Manifestly invariant superfield techniques are employed. A finite set of basic Nambu-Goldstone superfields is singled out by imposing infinitely many covariant constraints on the relevant Cartan 1-forms. The resulting superfield equations of motion and off-shell irreducibility conditions have a universal form for any N . We solve the irreducibility conditions on-shell for arbitrary N and off-shell for N ⩽ 4. The N = 3 and N = 4 models are examined in detail. These are the first examples of self-contained lagrangian models respecting superconformal symmetry with non- canonical generators (spontaneously broken). A generalization to the heterotic case and possible implications in the string theory are briefly outlined.

ABC of N=8,d=1 supermultiplets

Abstract We construct a variety of off-shell N = 8 , d = 1 supermultiplets with finite numbers of component fields as direct sums of properly constrained N = 4 , d = 1 superfields. We also show how these multiplets can be described in N = 8 , d = 1 superspace where the whole amount of supersymmetry is manifest. Some of these multiplets can be obtained by dimensional reduction from N = 2 multiplets in d = 4 , whereas others cannot. We give examples of invariant superfield actions for the multiplets constructed, including N = 8 superconformally invariant ones.

AdS2/CFT1, canonical transformations and superconformal mechanics

Abstract We propose a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS2×S2 horizon of an extreme Reissner–Nordstrom black hole. The equivalence holds for any finite value of the black hole mass and with both the radial and angular degrees of freedom of the particle taken into account. It is ensured by the existence of a canonical transformation in the Hamiltonian formalism. Using this transformation, we construct the Hamiltonian of a N=4 superparticle on AdS2×S2 background.

Partial supersymmetry breaking in N=4 supersymmetric quantum mechanics

The authors present a simple d=1 model of N=4 supersymmetric quantum mechanics (SQM) in which N=4 supersymmetry can be spontaneously broken down to N=2. When both SU(2) automorphism symmetries of N=4 1D supertranslation algebra are explicitly broken, this superalgebra acquires a constant central charge proportional to the product of two SU(2) breaking parameters. Due to this crucial property, no contradiction arises with Wittens theorem (1989) forbidding the partial spontaneous supersymmetry breaking in SQM models based on standard (having no central charges) 1D supertranslation algebras. For the partial breaking to really come about, it also proves necessary to consider the most general class of N=4, d=1 SQM Hamiltonians involving the terms quartic in fermion fields. They show that after performing a duality transformation these models can be interpreted as resulting from certain U(1) invariant N=2 2D Kahler sigma models via the Scherk-Schwartz-type dimensional reduction (1979).

Hidden symmetries of integrable conformal mechanical systems

Abstract We split the generic conformal mechanical system into a “radial” and an “angular” part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We reduce the analysis of the constants of motion of the full system to the study of certain differential equations on this orbit. For integrable mechanical systems, the conformal invariance renders them superintegrable, yielding an additional series of conserved quantities originally found by Wojciechowski in the rational Calogero model. Finally, we show that, starting from any N = 4 supersymmetric “angular” Hamiltonian system one may construct a new system with full N = 4 superconformal D ( 1 , 2 ; α ) symmetry.

N=8 superconformal mechanics

We construct new models of N=8 superconformal mechanics associated with the off-shell N=8, d=1 supermultiplets (3,8,5) and (5,8,3). These two multiplets are derived as N=8 Goldstone superfields and correspond to nonlinear realizations of the N=8, d=1 superconformal group OSp(4★|4) in its supercosets OSp(4★|4)U(1)R⊗SO(5) and OSp(4★|4)SU(2)R⊗SO(4), respectively. The irreducibility constraints for these superfields automatically follow from appropriate superconformal covariant conditions on the Cartan superforms. The N=8 superconformal transformations of the superspace coordinates and the Goldstone superfields are explicitly given. Interestingly, each N=8 supermultiplet admits two different off-shell N=4 decompositions, with different N=4 superconformal subgroups SU(1,1|2) and OSp(4★|2) of OSp(4★|4) being manifest as superconformal symmetries of the corresponding N=4, d=1 superspaces. We present the actions for all such N=4 splittings of the N=8 multiplets considered.

Towards the complete N=2 superfield Born-Infeld action with partially broken N=4 supersymmetry

We propose a systematic way of constructing N = 2, d = 4 superfield Born-Infeld action with a second nonlinearly realized N = 2 supersymmetry. The latter, together with the manifest N = 2 supersymmetry, form a central-charge extended N = 4, d = 4 supersymmetry. We embed the Goldstone-Maxwell N = 2 multiplet into an infinite-dimensional off-shell supermultiplet of this N = 4 supersymmetry and impose an infinite set of covariant constraints which eliminate all extra N = 2 superfields through the Goldstone-Maxwell one. The Born-Infeld superfield Lagrangian density is one of these composite superfields. The constraints can be solved by iterations to any order in the fields. We present the sought N = 2 Born-Infeld action up to the 10th order. It encompasses the action found earlier by Kuzenko and Theisen to the 8th order from a self-duality requirement. This is a strong indication that the complete N = 2 Born-Infeld action with partially broken N = 4 supersymmetry is also self-dual.

PARTIAL BREAKING OF N = 1, D = 10 SUPERSYMMETRY

Abstract We describe the spontaneous partial breaking of N=1, D=10 supersymmetry to N=(1,0), d=6 and its dimensionally-reduced versions in the framework of nonlinear realizations. The basic Goldstone superfield is N=(1,0), d=6 hypermultiplet superfield satisfying a nonlinear generalization of the standard hypermultiplet constraint. We interpret the generalized constraint as the manifestly worldvolume supersymmetric form of equations of motion of the type I super 5-brane in D=10. The related issues we address are a possible existence of brane extension of off-shell hypermultiplet actions, the possibility to utilize vector N=(1,0), d=6 supermultiplet as the Goldstone one, and the description of 1/4 breaking of N=1, D=11 supersymmetry.