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

Abstract

Proceeding from nonlinear realizations of the most general N = 4, d = 1 superconformal symmetry associated with the supergroup D(2, 1; α), 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.

A Journey Through Garden Algebras

“…This condition relates L I to the hermitian conjugate of R I , namely R I † , defined as usual by φ, R I (ψ) VL = R † I (φ), ψ VR (8) so that…”

“…In order to discuss this ins a way that brings this discussion in line with that of [8], we adhere to a convention that list three numbers (P B, P F, AB)…”

“…An enlightening example will be useful. By a proper counting of irreducible representation dimension for the EGR (8,8), we are left with {U L } ⊕ {M L } type Clifford algebraic superfield…”

“…As an illustration of these, the discussion will now treat such a case for GR (8,8). It may be verified that a suitable representation is provided by the 8 × 8 matrices…”

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].…”