New type of N = 4 supersymmetric quantum mechanics

Abstract

Abstract. We overview a new type of supersymmetric quantum mechanics models based on the worldline realizations of the supergroup SU(2|1). Our main focus is on the models associated with the chiral multiplets (2, 4, 2). Considering two nonequivalent deformations of the standard N = 4, d = 1 superspace, we define the relevant chiral superfields and construct their SU(2|1) invariant actions. We give off-and on-shell descriptions of these models and perform their quantization. The basic peculiarities of such models and interrelations between them are briefly discussed.

Massive quiver matrix models for massive charged particles in AdS

“…In particular, their (2, 4, 2) multiplet corresponds to our chiral multiplets, but they have Lagrangian expressions for an arbitrary Kähler potential. After changing to the ρ = 1 R-frame and removing all instances of the vector multiplets, our chiral Lagrangian agrees with equation (5.11) of [19] with the choice of a flat Kähler potential. On the other hand, our superpotential is arbitrary up to R-symmetry constraints.…”

“…We note that the chiral multiplet part of the massive quiver matrix mechanics Lagrangian in equation (2.1) has been given before, as part of a systematic construction of supersymmetric quantum mechanics models with su(2|1) supersymmetry [19,20]. This part can also be obtained by dimension reduction of the general four-dimensional N = 1 chiral multiplet Lagrangian of [21] on R × S 3 , and it has been obtained this way in [22], for the purpose of computing Casimir energies in conformal field theories on curved spaces.…”

“…The massive quiver Lagrangian in equation (2.1) is a special case of these models as is the BMN matrix model (see 3.2.4). We explain how to perform the dimensional reduction in section 5 and give additional details in appendix F. In section 5.6, we give a more detailed comparison of our models and those given in the works [19,20].…”

“…The superalgebra for the massive quiver matrix models is su(2|1) u(1) R in the ρ = 0 frame, as noted in appendix D. If no R-symmetry is present, one is restricted to the ρ = 0 frame and simply drops the u(1) R factor and the R-generator. Quantum mechanics with su(2|1) symmetry has been studied before [19,20]. The algebra listed in equation (2.1) of [19] is our algebra in the ρ = 1 frame.…”

“…Quantum mechanics with su(2|1) symmetry has been studied before [19,20]. The algebra listed in equation (2.1) of [19] is our algebra in the ρ = 1 frame. 12 The supersymmetries are time-independent and consequently the superalgebra is a centrally extended su(2|1) where the Hamiltonian plays the role of the central charge.…”