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WDVV Equations for 6d Seiberg–Witten Theory and Bi-Elliptic Curves

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Abstract

We present a generic derivation of the WDVV equations for 6d Seiberg–Witten theory, and extend it to the families of bi-elliptic spectral curves. We find that the elliptization of the naive perturbative and nonperturbative 6d systems roughly “doubles” the number of moduli describing the system.

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References

  1. Witten, E.: Nucl. Phys. B 340, 281 (1990)

    Article  MathSciNet  Google Scholar 

  2. Dijkgraaf, R., Verlinde, H., Verlinde, E.: Nucl. Phys. B 352, 59 (1991)

    Article  MathSciNet  Google Scholar 

  3. Marshakov, A., Mironov, A., Morozov, A.: Phys. Lett. B 389, 43 (1996) [arXiv:hep-th/9607109]

    Article  MathSciNet  Google Scholar 

  4. Dubrovin, B.: In: Integrable Systems and Quantum Groups, Montecatini Terme, 1993. Lecture Notes in Mathematics, vol. 1620, pp. 120–348. Springer, New York (1996) [arXiv:hep-th/9407018]

    Chapter  Google Scholar 

  5. Marshakov, A., Mironov, A., Morozov, A.: Mod. Phys. Lett. A 12, 773 (1997) [arXiv:hep-th/9701014]

    Article  MATH  MathSciNet  Google Scholar 

  6. Marshakov, A., Mironov, A., Morozov, A.: Int. J. Mod. Phys. A 15, 1157 (2000) [arXiv:hep-th/9701123]

    MATH  MathSciNet  Google Scholar 

  7. Morozov, A.: Phys. Lett. B 427, 93–96 (1998) [arXiv:hep-th/9711194]

    Article  MathSciNet  Google Scholar 

  8. Mironov, A., Morozov, A.: Phys. Lett. B 424, 48–52 (1998) [arXiv:hep-th/9712177]

    Article  MathSciNet  Google Scholar 

  9. de Wit, B., Marshakov, A.: Theor. Math. Phys. 129, 1504 (2001) [arXiv:hep-th/0105289]

    Article  MATH  Google Scholar 

  10. Krichever, I.: Commun. Pure. Appl. Math. 47, 437 (1992) [arXiv:hep-th/9205110]

    Article  MathSciNet  Google Scholar 

  11. Mironov, A.: The review in the book [17], [arXiv:hep-th/9903088]

  12. Boyarsky, A., Marshakov, A., Ruchayskiy, O., Wiegmann, P., Zabrodin, A.: Phys. Lett. B 515, 483–492 (2001) [arXiv:hep-th/0105260]

    Article  MATH  MathSciNet  Google Scholar 

  13. Marshakov, A.: In: Kazakov, D., Gladyshev, A. (eds.) Supersymmetry and Unification of Fundamental Interactions, pp. 370–381. World Scientific, Singapore (2002) [arXiv:hep-th/0108023]

    Google Scholar 

  14. Marshakov, A.: Theor. Math. Phys. 132, 895 (2002) [arXiv:hep-th/0201267]

    Article  MATH  MathSciNet  Google Scholar 

  15. Seiberg, N., Witten, E.: Nucl. Phys. B 426, 19 (1994) [arXiv:hep-th/9407087]

    Article  MATH  MathSciNet  Google Scholar 

  16. Marshakov, A.: Seiberg–Witten Theory and Integrable Systems. World Scientific, Singapore (1999)

    MATH  Google Scholar 

  17. Braden, H.W., Krichever, I. (eds.): Integrability: The Seiberg–Witten and Whitham Equations. Gordon and Breach, London (2000)

    MATH  Google Scholar 

  18. Marshakov, A.: Theor. Math. Phys. 112, 791 (1997) [arXiv:hep-th/9702083]

    Article  MATH  MathSciNet  Google Scholar 

  19. Donagi, R.: In: Survey of Differential Geometry, vol. IV. Int. Press, Boston (1998) [arXiv:alg-geom/9705010]

    Google Scholar 

  20. Krichever, I.M., Phong, D.H.: In: Survey of Differential Geometry, vol. IV. Int. Press, Boston (1998) [arXiv:hep-th/9708170]

    Google Scholar 

  21. Gorsky, A., Mironov, A.: [arXiv:hep-th/0011197]

  22. Gorsky, A., Marshakov, A., Mironov, A., Morozov, A.: [arXiv:hep-th/9604078]

  23. Marshakov, A., Mironov, A.: Nucl. Phys. B 518, 59 (1998) [arXiv:hep-th/9711156]

    Article  MATH  MathSciNet  Google Scholar 

  24. Riley, A., Strachan, I.: [arXiv:math-ph/0511048]

  25. Braden, H.W., Marshakov, A., Mironov, A., Morozov, A.: Nucl. Phys. B 573, 553–572 (2000) [arXiv:hep-th/9906240]

    Article  MATH  MathSciNet  Google Scholar 

  26. Inozemtsev, V.: Comm. Math. Phys. 121, 629 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  27. Itoyama, H., Morozov, A.: Nucl. Phys. B 491, 529 (1997) [arXiv:hep-th/9512161]

    Article  MATH  MathSciNet  Google Scholar 

  28. Ito, K., Yang, S.-K.: Phys. Lett. B 433, 56–62 (1998) [arXiv:hep-th/9803126]

    Article  MathSciNet  Google Scholar 

  29. Hoevenaars, L., Martini, R.: Lett. Math. Phys. 57, 175–183 (2001) [arXiv:hep-th/0102190]

    Article  MATH  MathSciNet  Google Scholar 

  30. Donagi, R., Witten, E.: Nucl. Phys. B 460, 299 (1996) [arXiv:hep-th/9510101]

    Article  MATH  MathSciNet  Google Scholar 

  31. Martinec, E.: Phys. Lett. B 367, 91–96 (1996) [arXiv:hep-th/9510204]

    Article  MathSciNet  Google Scholar 

  32. Gorsky, A., Marshakov, A.: Phys. Lett. B 375, 127 (1996) [arXiv:hep-th/9510224]

    Article  MATH  MathSciNet  Google Scholar 

  33. Itoyama, H., Morozov, A.: Nucl. Phys. B 477, 855 (1996) [arXiv:hep-th/9511126; arXiv:hep-th/9601168]

    Article  MATH  MathSciNet  Google Scholar 

  34. D’Hoker, E., Phong, D.H.: Nucl. Phys. B 513, 405 (1998) [arXiv:hep-th/9709053]

    Article  MATH  MathSciNet  Google Scholar 

  35. Gorsky, A., Krichever, I., Marshakov, A., Mironov, A., Morozov, A.: Phys. Lett. B 355, 466 (1995) [arXiv:hep-th/9505035]

    Article  MATH  MathSciNet  Google Scholar 

  36. Mironov, A., Morozov, A.: Phys. Lett. B 475, 71–76 (2000) [arXiv:hep-th/9912088]

    Article  MATH  MathSciNet  Google Scholar 

  37. Mironov, A., Morozov, A.: [arXiv:hep-th/0001168]

  38. Braden, H.W., Hollowood, T.: JHEP 12, 023 (2003) [arXiv:hep-th/0311024]

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, University of Edinburgh, Edinburgh, Scotland, UK

    H. W. Braden

  2. Lebedev Physics Institute, Moscow, Russia

    A. Marshakov & A. Mironov

  3. ITEP, Moscow, Russia

    A. Marshakov, A. Mironov & A. Morozov

Authors
  1. H. W. Braden
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  2. A. Marshakov
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  3. A. Mironov
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  4. A. Morozov
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Correspondence to H. W. Braden.

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Braden, H.W., Marshakov, A., Mironov, A. et al. WDVV Equations for 6d Seiberg–Witten Theory and Bi-Elliptic Curves. Acta Appl Math 99, 223–244 (2007). https://doi.org/10.1007/s10440-007-9164-4

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  • DOI: https://doi.org/10.1007/s10440-007-9164-4

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