Abstract
By introduction of an additional variable and addition of a Weyl invariant correction term to the perturbative prepotential in five-dimensional Seiberg-Witten theory we construct solutions of the Witten–Dijkgraaf–Verlinde–Verlinde equations of trigonometric type for all crystallographic root systems.
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References
Witten, E.: Two-dimensional gravity and intersection theory on moduli space, In: Surveys in Differential Geometry, Cambridge, MA, 1990, pp. 243–310.
Dijkgraaf, R., Verlinde, E. and Verlinde, H.: Topological strings in dj 1, Nuclear Phys. B 352 (1991), 59–86.
Dijkgraaf, R.: Les Houches lectures on elds, strings and duality, hep-th/9703136.
Marshakov, A., Mironov, A. and Morozov, A.: More evidence for the WDVV equations in N= 2 SUSY Yang–Mills theories, Internat. J. Modern Phys. A 15(8)(2000), 1157–1206.
Nekrasov, N.: Five-dimensional gauge theories and relativistic integrable systems, Nuclear Phys. B 531 (1998), 323–344.
Mironov, A.: WDVV equations and Seiberg–Witten theory, In: Integrability: The Seiberg–Witten and Whitham Equations, Gordon and Breach, Amsterdam, 2000, pp. 103–123.
Dubrovin, B.: Geometry of 2 D topological field theories, In: Integrable Systems and Quantum Groups (Montecatini Terme, 1993), Lecture Notes in Math. 1620, Springer, Berlin, 1996, pp. 120–348, hep-th/9407018.
Martini, R. and Gragert, P. K. H.: Solutions of WDVV equations in Seiberg–Witten theory from root systems, J. Nonlinear Math. Phys. 6(1)(1999), 1–4, hep-th/9901166.
Hoevenaars, L. K. and Martini, R.: On the WDVV equations in vedimensional gauge theories, math-ph/0212016.
Matsuo, A.: Integrable connections to zonal spherical functions, Invent. Math. 110 (1992), 95–121.
Bourbaki, N.: Groupes et alge`bres de Lie, Chapitres 4-6, Hermann, Paris, 1969.
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Martini, R., Hoevenaars, L.K. Trigonometric Solutions of the WDVV Equations from Root Systems. Letters in Mathematical Physics 65, 15–18 (2003). https://doi.org/10.1023/A:1027389032533
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DOI: https://doi.org/10.1023/A:1027389032533