New realizations of the supergroup D(2, 1; α) in N = 4 $$ \mathcal{N}=4 $$ superconformal mechanics

Abstract

We present new explicit realizations of the most general N = 4, d = 1 superconformal symmetry D(2, 1; α) in the models of N = 4 superconformal mechanics based on the reducible multiplets (1, 4, 3) ⊕ (0, 4, 4), (3, 4, 1) ⊕ (0, 4, 4) and (4, 4, 0) ⊕ (0, 4, 4). We start from the manifestly supersymmetric superfield actions for these systems and then descend to the relevant off-and on-shell component actions from which we derive the D(2, 1; α) (super)charges by the Noether procedure. Some peculiarities of these realizations of D(2, 1; α) are discussed. We also construct a new D(2, 1; α) invariant system by joining the multiplets (3, 4, 1) and (4, 4, 0) in such a way that they interact with each other through an extra (0, 4, 4) multiplet. New fermionic conformal couplings appear as the result of elimination of the appropriate auxiliary fields.

Super 0-brane action on the coset space of D(2, 1; α) supergroup

“…It should be mentioned that SU(1, 1|2) is a particular instance of the most general d = 1, N = 4 superconformal group D(2, 1; α) which arises at α = −1. Although D(2, 1; α)superconformal mechanics has been extensively studied in the past [1], [43]- [50], a link to the near horizon black hole geometries has been established only quite recently [51]. In particular, a canonical transformation which relates D(2, 1; α)-superconformal mechanics based upon supermultiplets of the type (3,4,1) and (4,4,0) to BP S-superparticles propagating near the horizon of the extreme Reissner-Nordström-AdS-dS black hole in four and five dimensions has been found.…”

Superfield approach to higher derivative $$ \mathcal{N} $$ = 1 superconformal mechanics

“…• list all the polynomials P (n) ij in (14) which correspond to the given order of a dynamical system;…”

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]).…”