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Darboux coordinates and instanton corrections in projective superspace

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Abstract

By demanding consistency of the Legendre transform construction of hyperkähler metrics in projective superspace, we derive the expression for the Darboux coordinates on the hyperkähler manifold. We apply these results to study the Coulomb branch moduli space of 4D, \( \mathcal{N}=2 \) super-Yang-Mills theory (SYM) on \( {{\mathbb{R}}^3}\times {S^1} \), recovering the results by GMN. We also apply this method to study the electric corrections to the moduli space of 5D, \( \mathcal{N}=1 \) SYM on \( {{\mathbb{R}}^3}\times {T^2} \) and give the Darboux coordinates explicitly.

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Authors and Affiliations

  1. C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY, 11790-3840, U.S.A.

    P. Marcos Crichigno & Dharmesh Jain

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  1. P. Marcos Crichigno
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  2. Dharmesh Jain
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Correspondence to P. Marcos Crichigno.

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ArXiv ePrint: 1204.3899

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Crichigno, P.M., Jain, D. Darboux coordinates and instanton corrections in projective superspace. J. High Energ. Phys. 2012, 27 (2012). https://doi.org/10.1007/JHEP10(2012)027

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