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arXiv · 2303.14675

$(0,4)$ Projective Superspaces I: Interacting Linear Sigma Models

Naveen S. Prabhakar·Martin Roček
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Abstract

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 $\text{SU}(2)$ in the R-symmetry $\text{SU}(2) \times \text{SU}(2)$ which are interpreted as homogeneous coordinates on $\mathbf{CP}^1 \times \mathbf{CP}^1$. The superfields are analytic in the $\mathbf{CP}^1$ 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 $\mathbf{R}^4$ with a Yang-Mills instanton solution. The hyperk\"ahler 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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Naveen S. Prabhakar, Martin Roček. 2023-03-26. $(0,4)$ Projective Superspaces I: Interacting Linear Sigma Models. https://doi.org/10.1007/jhep07(2023)117

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