Higher genus superstring amplitudes from the geometry of moduli space. (English) Zbl 1192.81280
Summary: We show that the higher genus 4-point superstring amplitude is strongly constrained by the geometry of moduli space of Riemann surfaces. A detailed analysis leads to a natural proposal which satisfies several conditions. The result is based on the recently derived Siegel induced metric on the moduli space of Riemann surfaces and on combinatorial products of determinants of holomorphic Abelian differentials.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 32G81 | Applications of deformations of analytic structures to the sciences |
| 11Z05 | Miscellaneous applications of number theory |
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
References:
| [1] | D’Hoker, E.; Phong, D. H., Nucl. Phys. B, 715, 91 (2005) · Zbl 1207.81110 |
| [2] | D’Hoker, E.; Phong, D. H., Nucl. Phys. B, 715, 3 (2005) · Zbl 1207.81111 |
| [3] | D’Hoker, E.; Gutperle, M.; Phong, D. H. |
| [4] | Berkovits, N. |
| [5] | Berkovits, N., JHEP, 0503, 041 (2005) · Zbl 0976.81046 |
| [6] | Berkovits, N.; Nekrasov, N. |
| [7] | Oda, I.; Tonin, M. · Zbl 1247.81509 |
| [8] | Matone, M.; Mazzucato, L.; Oda, I.; Sorokin, D.; Tonin, M., Nucl. Phys. B, 639, 182 (2002) · Zbl 0997.81082 |
| [9] | Grassi, P. A.; Policastro, G.; van Nieuwenhuizen, P. · Zbl 1006.81072 |
| [10] | Grassi, P. A.; van Nieuwenhuizen, P., Phys. Lett. B, 610, 129 (2005) · Zbl 1247.81507 |
| [11] | Chandia, O.; Vallilo, B. C., JHEP, 0404, 041 (2004) |
| [12] | Trivedi, G., Mod. Phys. Lett. A, 17, 2239 (2002) · Zbl 1083.81580 |
| [13] | Schiappa, R.; Wyllard, N. |
| [14] | Aisaka, Y.; Kazama, Y. |
| [15] | Cornalba, L.; Costa, M. S.; Schiappa, R. |
| [16] | Mukhopadhyay, P. |
| [17] | Iengo, R.; Zhu, C. J., Phys. Lett. B, 212, 313 (1988) |
| [18] | Zheng, Z. J.; Wu, J. B.; Zhu, C. J., Nucl. Phys. B, 663, 95 (2003) · Zbl 1060.81596 |
| [19] | Zhu, C. J. |
| [20] | Matone, M.; Volpato, R. |
| [21] | Green, M. B.; Vanhove, P., Phys. Rev. D, 61, 104011 (2000) |
| [22] | Arbarello, E.; Cornalba, M.; Griffiths, P. A.; Harris, J., Geometry of Algebraic Curves, vol. 1 (1985), Springer: Springer Berlin · Zbl 0559.14017 |
| [23] | Beilinson, A. A.; Manin, Y. I., Commun. Math. Phys., 107, 359 (1986) · Zbl 0604.14016 |
| [24] | D’Hoker, E.; Phong, D. H., Rev. Mod. Phys., 60, 917 (1988) |
| [25] | Morozov, A., Phys. Lett. B, 184, 171 (1987) |
| [26] | Matone, M., Lett. Math. Phys., 33, 75 (1995) · Zbl 0844.14015 |
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