Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of solutions of the WDVV equations

Ferguson, J. and Strachan, I.A.B. (2008) Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of solutions of the WDVV equations. Communications in Mathematical Physics, 280(1), pp. 1-25. (doi: 10.1007/s00220-008-0464-y)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Strachan, Professor Ian
• Authors: Ferguson, J., and Strachan, I.A.B.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Communications in Mathematical Physics
• ISSN: 0010-3616
• ISSN (Online): 1432-0916
• Published Online: 15 March 2008
• Copyright Holders: Copyright © 2008 Springer
• First Published: First published in Communications in Mathematical Physics 2008 280(1):1-25
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher