Abstract
In this paper, we quantize superconformal models defined by worldline supermultiplets. Two types of superconformal mechanics, with and without a De Alfaro Fubini Furlan (DFF) term, are considered. Without a DFF term (Calogero potential only), the supersymmetry is unbroken. The models with a DFF term correspond to deformed (if the Calogero potential is present) or undeformed oscillators. For these (un)deformed oscillators, the classical invariant superconformal algebra acts as a spectrum-generating algebra of the quantum theory. Besides the examples, we explicitly quantize the superconformally invariant worldline models defined by the (1, 4, 3) supermultiplet [with invariance, for ] and by the (2, 2, 0) supermultiplet [with two-dimensional target and invariance]. The parameter is the scaling dimension of the (1, 4, 3) supermultiplet and, in the DFF case, has a direct interpretation as a vacuum energy. In the DFF case, for the models, the scaling dimension is quantized (either or ). The ordinary two-dimensional oscillator is recovered, after imposing a superselection restriction, from the model. In particular, a single bosonic vacuum is selected. The spectrum of the unrestricted two-dimensional theory is decomposed into an infinite set of lowest-weight representations of . Extra fermionic raising operators, not belonging to the original superalgebra, allow (for ) to construct the whole spectrum from the two degenerate (one bosonic and one fermionic) vacua.
- Received 11 April 2017
DOI:https://doi.org/10.1103/PhysRevD.96.065014
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