(0, 4) Projective superspaces. Part I. Interacting linear sigma models

Naveen Prabhakar (International Centre for Theoretical Sciences-TIFR, Shivakote, Bengaluru, 560089, India) ; Martin Roček (C.N. Yang Institute of Theoretical Physics, Stony Brook University, Stony Brook, NY, 11794-3840, USA)

We describe the projective superspace approach to supersymmetric models with off-shell (0, 4) supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables — one doublet for each SU(2) in the R-symmetry SU(2) × SU(2) which are interpreted as homogeneous coordinates on CP 1 × CP 1. The superfields are analytic in the CP 1 coordinates and this analyticity plays an important role in our description. For instance, it leads to stringent constraints on the interactions one can write down for a given superfield content of the model. As an example, we describe in projective superspace Witten’s ADHM sigma model — a linear sigma model with non-derivative interactions whose target is R 4 with a Yang-Mills instanton solution. The hyperkähler nature of target space and the twistor description of instantons by Ward, and Atiyah, Hitchin, Drinfeld and Manin are natural outputs of our construction.

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      "source": "Springer", 
      "value": "We describe the projective superspace approach to supersymmetric models with off-shell (0, 4) supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables \u2014 one doublet for each SU(2) in the R-symmetry SU(2) \u00d7 SU(2) which are interpreted as homogeneous coordinates on CP 1 \u00d7 CP 1. The superfields are analytic in the CP 1 coordinates and this analyticity plays an important role in our description. For instance, it leads to stringent constraints on the interactions one can write down for a given superfield content of the model. As an example, we describe in projective superspace Witten\u2019s ADHM sigma model \u2014 a linear sigma model with non-derivative interactions whose target is R 4 with a Yang-Mills instanton solution. The hyperk\u00e4hler nature of target space and the twistor description of instantons by Ward, and Atiyah, Hitchin, Drinfeld and Manin are natural outputs of our construction."
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Published on:
13 July 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 7
Pages 1-50
DOI:
https://doi.org/10.1007/JHEP07(2023)117
arXiv:
2303.14675
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: