Higher Order Deformations of Complex Structures
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 va...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147114 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862580255063015424 |
|---|---|
| author | D'Hoker, E. Phong, D.H. |
| author_facet | D'Hoker, E. Phong, D.H. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-26T19:15:36Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147114 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T19:15:36Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | D'Hoker, E. Phong, D.H. 2019-02-13T16:53:34Z 2019-02-13T16:53:34Z 2015 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. 1815-0659 2010 Mathematics Subject Classification: 32G05; 51M15; 51P05; 53Z05 DOI:10.3842/SIGMA.2015.047 https://nasplib.isofts.kiev.ua/handle/123456789/147114 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Higher Order Deformations of Complex Structures Article published earlier |
| spellingShingle | Higher Order Deformations of Complex Structures D'Hoker, E. Phong, D.H. |
| title | Higher Order Deformations of Complex Structures |
| title_full | Higher Order Deformations of Complex Structures |
| title_fullStr | Higher Order Deformations of Complex Structures |
| title_full_unstemmed | Higher Order Deformations of Complex Structures |
| title_short | Higher Order Deformations of Complex Structures |
| title_sort | higher order deformations of complex structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147114 |
| work_keys_str_mv | AT dhokere higherorderdeformationsofcomplexstructures AT phongdh higherorderdeformationsofcomplexstructures |