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Higher Order Deformations of Complex Structures
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Higher Order Deformations of Complex Structures
Інший ID:
2010 Mathematics Subject Classification: 32G05; 51M15; 51P05; 53Z05
DOI:10.3842/SIGMA.2015.047
DOI:10.3842/SIGMA.2015.047
Посилання:
Higher Order Deformations of Complex Structures / E. D'Hoker, D.H. Phong // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 19 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
We would like to acknowledge the organizers, Decio Levi, Willard Miller, Yvan Saint-Aubin,
and Pavel Winternitz for inviting us to the enjoyable conference and celebration in honor of Luc
Vinet at the Centre de Recherches Math´ematiques. We would also like to thank the referees for
their very careful reading of the paper. This research was supported in part by the National
Science Foundation grants PHY-13-13986 and DMS-12-66033.
Дата:
2015
Переглядів:
440
Завантажень:
226
Анотація:
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and correlation functions in conformal field theories with vanishing total central charge. The stress tensor is shown to give a simple representation of these deformations valid to all orders. Such deformation formulas naturally enter into the evaluation of superstring amplitudes at two-loop order with Ramond punctures, and at higher loop order, in the supergravity formulation of the RNS superstring.
