From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(2|1) models

I. E. Cunha, N. L. Holanda, and F. Toppan
Phys. Rev. D 96, 065014 – Published 20 September 2017

Abstract

In this paper, we quantize superconformal σ 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 osp(1|2) examples, we explicitly quantize the superconformally invariant worldline σ models defined by the N=4 (1, 4, 3) supermultiplet [with D(2,1;α) invariance, for α0,1] and by the N=2 (2, 2, 0) supermultiplet [with two-dimensional target and sl(2|1) invariance]. The parameter α 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 sl(2|1) models, the scaling dimension λ is quantized (either λ=12+Z or λ=Z). The ordinary two-dimensional oscillator is recovered, after imposing a superselection restriction, from the λ=12 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 sl(2|1). Extra fermionic raising operators, not belonging to the original sl(2|1) superalgebra, allow (for λ=12+Z) to construct the whole spectrum from the two degenerate (one bosonic and one fermionic) vacua.

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  • Received 11 April 2017

DOI:https://doi.org/10.1103/PhysRevD.96.065014

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

I. E. Cunha*, N. L. Holanda, and F. Toppan

  • CBPF, Rua Dr. Xavier Sigaud 150, Urca, CEP 22290-180 Rio de Janeiro (RJ), Brazil

  • *ivanec@cbpf.br
  • linneu@cbpf.br
  • toppan@cbpf.br

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Vol. 96, Iss. 6 — 15 September 2017

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