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

Abstract

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 N =4 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 S 3 → S 2 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.

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(Cunha1, Holanda2, Toppan3 2017Phys. Rev. D162100View full textAdd to dashboardCite

“…For this value the invariant superalgebra is D(2, 1; − 1 2 ) = D(2, 1) ≈ osp(4|2). The results about the quantum parabolic D(2, 1; α) models coincide with those obtained, with different methods, in [4]. The new feature, in the present paper, is the construction of the quantum trigonometric models which, so far, have not been investigated.…”

“…We present here the quantization of this model repeating the same steps discussed in Section 4 for the osp(1|2)-invariant model. In this subsection we recover, within a different framework, the models discussed in [4].…”

SU(1, 1|N) superconformal mechanics with fermionic gauge symmetry

“…In particular, it was argued in [1,4] that superconformal mechanics may provide a microscopic quantum description of extreme black holes. Motivated by this proposal a plenty of SU(1, 1|2) superconformal one-dimensional systems and their D(2, 1; α) extensions have been constructed [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. A related line of research concerns the study of superconformal particles propagating on near horizon black hole backgrounds [25][26][27][28][29][30][31][32][33][34].…”

“…There are several competing approaches to the construction of superconformal mechanics: the superfield approach [10,14,[16][17][18][19][20][21][22]35], the method of nonlinear realizations [5,9,25,34], and the canonical formalism (e.g. [29,37,45]).…”

A world-line framework for 1D topological conformal σ-models

“…untwisted) superconformal mechanics [16,17], its model building and its applications (which range from AdS 2 /CF T 1 correspondence, nearhorizon geometry of extremal black holes, etc.). One can consult the two review papers [18,19] and the references therein.…”