Sergey Fedoruk

Supersymmetric Calogero models by gauging

New superconformal extensions of d = 1 Calogero-type systems are obtained by gauging the U(n) isometry of matrix superfield models. We consider the cases of N = 1, N = 2, and N = 4 as one-dimensional supersymmetries. The bosonic core of the N = 1 and N = 2 models is the standard conformal A n―1 Calogero system, whereas the N = 4 model is an extension of the U(2)-spin Calogero system.

OSp(4|2) superconformal mechanics

A new superconformal mechanics with OSp(4|2) symmetry is obtained by gauging the U(1) isometry of a superfield model. It is the one-particle case of the new = 4 super Calogero model recently proposed in arXiv:0812.4276 [hep-th]. Classical and quantum generators of the osp(4|2) superalgebra are constructed on physical states. As opposed to other realizations of = 4 superconformal algebras, all supertranslation generators are linear in the odd variables, similarly to the = 2 case. The bosonic sector of the component action is standard one-particle (dilatonic) conformal mechanics accompanied by an SU(2)/U(1) Wess-Zumino term, which gives rise to a fuzzy sphere upon quantization. The strength of the conformal potential is quantized.

New D(2, 1; α) mechanics with spin variables

We elaborate on a novel superconformal mechanics model possessing D(2, 1; α) symmetry and involving extra U(2) spin variables. It is the one-particle case of the

Two-twistor particle models and free massive higher spin fields

mathcal{N} = 4

Nahm equations in supersymmetric mechanics

superconformal matrix model recently proposed in arXiv:0812.4276 [hep-th], and it generalizes to arbitrary α≠0 the OSp(4|2) superconformal mechanics of arXiv:0905.4951 [hep-th]. As in the latter case, the U(2) spin variables are described by a Wess-Zumino action and define the first Hopf map S3 → S2 in the target space. Upon quantization, they represent a fuzzy sphere. We find the classical and quantum generators of the D(2, 1; α) superalgebra and their realization on the physical states. The super wavefunction encompasses various multiplets of the SU(2)R and SU(2)L subgroups of D(2, 1; α), with fixed isospins. The conformal potential is determined by the external magnetic field in the Wess-Zumino term, whose strength is quantized like in the OSp(4|2) case. As a byproduct, we reveal new invariant subspaces in the enveloping algebra of D(2, 1; α) for our quantum realization.

New super-Calogero models and OSp(4|2) superconformal mechanics

A bstractWe present D = 3 and D = 4 world-line models for massive particles moving in a new type of enlarged spacetime, with D−1 additional vector coordinates, which after quantization lead to towers of massive higher spin (HS) free fields. Two classically equivalent formulations are presented: one with a hybrid spacetime/bispinor variables and a second described by a free two-twistor dynamics with constraints. After first quantization in the D = 3 and D = 4 cases, the wave functions satisfying a massive version of Vasiliev’s free unfolded equations are given as functions on the SL(2, ℝ) and SL(2, ℂ) group manifolds respectively, which describe arbitrary on-shell momenta and spin degrees of freedom. Further we comment on the D = 6 case, and possible supersymmetric extensions are mentioned as well. Finally, the description of interactions and the AdS/CFT duality are briefly considered for massive HS fields.

New model of the higher spin particle

A bstractWe elaborate on a novel model of

Model of massless relativistic particle with continuous spin and its twistorial description

mathcal{N} = {4}

Quantum SU(2|1) supersymmetric Calogero-Moser spinning systems

supersymmetric mechanics with extra spin variables. A dynamical linear (1,4,3) multiplet is coupled to a “semi-dynamical” linear (3,4,1) multiplet representing spin degrees of freedom in a Wess-Zumino action. The unique coupling of these two multiplets relates the dynamical bosonic variable to an arbitrary harmonic function of the SU(2) triplet of spin variables. As we prove at the classical and quantum level,

Superconformal Calogero Models as a Gauged Matrix Mechanics

mathcal{N} = {4}