Quaternion-Kähler N $$ \mathcal{N} $$ = 4 supersymmetric mechanics
Evgeny Ivanov (0000000406204119, Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow region, Russia); Luca Mezincescu (0000 0004 1936 8606, Department of Physics, University of Miami, P.O. Box 248046, Coral Gables, FL, 33124, U.S.A.)
Using the N $$ \mathcal{N} $$ = 4, 1 D harmonic superspace approach, we construct a new type of N $$ \mathcal{N} $$ = 4 supersymmetric mechanics involving 4 n -dimensional Quaternion-Kähler (QK) 1 D sigma models as the bosonic core. The basic ingredients of our construction are local N $$ \mathcal{N} $$ = 4,1 D supersymmetry realized by the appropriate transformations in 1 D harmonic superspace, the general N $$ \mathcal{N} $$ = 4, 1 D superfield vielbein and a set of 2( n + 1) analytic âmatterâ superfields representing ( n + 1) off-shell supermultiplets ( 4 , 4 , 0 ). Both superfield and component actions are given for the simplest QK models with the manifolds âH n â=âSp(1, n )/[Sp(1)âÃâSp( n )] and âP n â=âSp(1â+â n )/[Sp(1)âÃâSp( n )] as the bosonic targets. For the general case the relevant superfield action and constraints on the ( 4 , 4 , 0 ) âmatterâ superfields are presented. Further generalizations are briefly discussed.
