Superconformal mechanics

Abstract

We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single-and multiparticle systems are covered.

New type of N = 4 supersymmetric quantum mechanics

“…Though the supercharges do not commute withH, they are still conserved due to the specific explicit dependence on t. This situation is reminiscent of what happens, e.g., in conformal and superconformal mechanics [8].…”

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(Cunha1, Holanda2, Toppan3 2017Phys. Rev. D172100View full textAdd to dashboardCite

“…Models of superconformal mechanics have been investigated in [5]- [13] (see, e.g., the review [14] and references therein). For superconformal actions with oscillator potentials see [15,16,1].…”

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

“…Let us discuss the issue of the κ-symmetry for N > 2. Varying the action (3.13), setting 14) and proceeding along the same lines as above, one obtains a system of the algebraic equations …”

“…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]).…”