A Journey Through Garden Algebras

Abstract

Summary. The main purpose of these lectures is to give a pedagogical overview on the possibility to classify and relate off-shell linear supermultiplets in the context of supersymmetric mechanics. A special emphasis is given to a recent graphical technique that turns out to be particularly effective for describing many aspects of supersymmetric mechanics in a direct and simplifying way. 2 S. Bellucci, S. J. Gates, Jr., E. Orazi

Gauging N=4 supersymmetric mechanics II: (1,4,3) models from the Delduc1, Ivanov2 2007Nuclear Physics B5031130View full textAdd to dashboardCite

“…Passing to the harmonic projections ω, l ++ and V ++(±±) , V ++(+−) by the same relations as in the previous Section, we observe that 6) where the involved analytic parameters are the proper projections ofΛ (ab) . Eqs.…”

The common origin of linear and nonlinear chiral multiplets in mechanics

“…It is the last possible two-parameter symmetry implementable on q +a . Thus we show that two known off-shell forms of the N =4, d=1 multiplet (2,4,2), the linear and nonlinear ones, in fact exhaust all possibilities.…”

“…The one-dimensional supersymmetry and related models of supersymmetric (quantum) mechanics reveal many specific surprising features and, at the same time, have a lot of links with higher-dimensional theories of current interest (see e.g. [1,2] and refs. therein).…”

“…They prove to naturally arise as a result of gauging some two-parameter isometry groups admitting a realization on the harmonic analytic superfield q +a which describes the multiplet (4,4,0). The origin of the difference between these two versions of the (2,4,2) multiplet is attributed to the fact that they emerge from gauging two essentially different isometries: the linear multiplet is associated with gauging of some purely shift isometries, while the nonlinear one corresponds to gauging the product of two "rotational" isometries, viz. the target space rescalings and a U(1) subgroup of the SU(2) Pauli-Gürsey group.…”

Unidexterously constrained worldsheet superfields

“…Nevertheless, it turns out that precisely this superfield on half-shell [19] may be employed to eliminate the highlighted unnamed nodes indicated in (10)-without incurring any worldsheet differential constraints on the remaining component fields. That is, the (on half-shell) lefton superfield Λ may be used to restrict an off-shell (1|4|6|4|1)-component intact superfield (5) to a proper offshell (1|4|5|2|0)-component superfield (14). This then also defines a strict morphism between these off-shell supermultiplets by the previously unexplored means of unidexterous Lagrange multipliers.…”