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Logarithmic Deformations of the Rational Superpotential/Landau-Ginzburg Construction of Solutions of the WDVV Equations

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Abstract

The superpotential in the Landau-Ginzburg construction of solutions to the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations is modified to include logarithmic terms. This results in deformations - quadratic in the deformation parameters- of the normal prepotential solutions of the WDVV equations. Such solutions satisfy various pseudo-quasi-homogeneity conditions, on assigning a notional weight to the deformation parameters. These solutions originate in the so-called ‘water-bag’ reductions of the dispersionless KP hierarchy. This construction includes, as a special case, deformations which are polynomial in the flat coordinates, resulting in a new class of polynomial solutions of the WDVV equations.

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  1. Department of Mathematics, University of Glasgow, Glasgow, G12 8QQ, UK

    James T. Ferguson & Ian A. B. Strachan

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  1. James T. Ferguson
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  2. Ian A. B. Strachan
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Correspondence to James T. Ferguson.

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Communicated by G.W. Gibbons

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Ferguson, J.T., Strachan, I.A.B. Logarithmic Deformations of the Rational Superpotential/Landau-Ginzburg Construction of Solutions of the WDVV Equations. Commun. Math. Phys. 280, 1–25 (2008). https://doi.org/10.1007/s00220-008-0464-y

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  • DOI: https://doi.org/10.1007/s00220-008-0464-y

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