Moving NS Punctures on Super Spheres
One of the subtleties that has made superstring perturbation theory intricate at high string loop order is the fact that, as shown by Donagi and Witten, supermoduli space is not holomorphically projected, nor is it holomorphically split. In recent years, Sen (further refined by Sen and Witten) has i...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212605 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Moving NS Punctures on Super Spheres. Dimitri P. Skliros. SIGMA 20 (2024), 090, 30 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862689575107821568 |
|---|---|
| author | Skliros, Dimitri P. |
| author_facet | Skliros, Dimitri P. |
| citation_txt | Moving NS Punctures on Super Spheres. Dimitri P. Skliros. SIGMA 20 (2024), 090, 30 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | One of the subtleties that has made superstring perturbation theory intricate at high string loop order is the fact that, as shown by Donagi and Witten, supermoduli space is not holomorphically projected, nor is it holomorphically split. In recent years, Sen (further refined by Sen and Witten) has introduced the notion of vertical integration in moduli space. This enables one to build BRST-invariant and well-defined amplitudes by adding certain correction terms to the contributions associated with the traditional ''delta function'' gauge fixing for the worldsheet gravitino on local patches. The Sen and Witten approach is made possible due to there being no obstruction to a smooth splitting of the supermoduli space, but it may not necessarily be the most convenient or natural solution to the problem. In particular, this approach does not determine what these correction terms actually are from the outset. Instead, it shows that such correction terms in principle exist, and when included, make all perturbative amplitudes well-defined. There may be situations, however, where one would like to instead have a well-defined and fully determined path integral at arbitrary string loop order from the outset. In this paper, I initiate an alternative (differential-geometric) approach that implements the fact that a smooth gauge slice for supermoduli space always exists. As a warmup, I focus specifically on super Riemann surfaces with the topology of a sphere in heterotic string theory, incorporating the corresponding super curvature locally, and introduce a new well-defined smooth gauge fixing that leads to a globally defined path integral measure that translates arbitrary fixed (−1) picture NS vertex operators (or handle operators) (that may or may not be offshell) to integrated (0) picture. I also provide some comments on the extension to arbitrary super Riemann surfaces.
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| first_indexed | 2026-03-17T20:08:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212605 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T20:08:19Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Skliros, Dimitri P. 2026-02-09T08:05:21Z 2024 Moving NS Punctures on Super Spheres. Dimitri P. Skliros. SIGMA 20 (2024), 090, 30 pages 1815-0659 2020 Mathematics Subject Classification: 32G05; 32G15; 51M15; 53Z05 arXiv:2307.06355 https://nasplib.isofts.kiev.ua/handle/123456789/212605 https://doi.org/10.3842/SIGMA.2024.090 One of the subtleties that has made superstring perturbation theory intricate at high string loop order is the fact that, as shown by Donagi and Witten, supermoduli space is not holomorphically projected, nor is it holomorphically split. In recent years, Sen (further refined by Sen and Witten) has introduced the notion of vertical integration in moduli space. This enables one to build BRST-invariant and well-defined amplitudes by adding certain correction terms to the contributions associated with the traditional ''delta function'' gauge fixing for the worldsheet gravitino on local patches. The Sen and Witten approach is made possible due to there being no obstruction to a smooth splitting of the supermoduli space, but it may not necessarily be the most convenient or natural solution to the problem. In particular, this approach does not determine what these correction terms actually are from the outset. Instead, it shows that such correction terms in principle exist, and when included, make all perturbative amplitudes well-defined. There may be situations, however, where one would like to instead have a well-defined and fully determined path integral at arbitrary string loop order from the outset. In this paper, I initiate an alternative (differential-geometric) approach that implements the fact that a smooth gauge slice for supermoduli space always exists. As a warmup, I focus specifically on super Riemann surfaces with the topology of a sphere in heterotic string theory, incorporating the corresponding super curvature locally, and introduce a new well-defined smooth gauge fixing that leads to a globally defined path integral measure that translates arbitrary fixed (−1) picture NS vertex operators (or handle operators) (that may or may not be offshell) to integrated (0) picture. I also provide some comments on the extension to arbitrary super Riemann surfaces. I am grateful to Eric D’Hoker, Edward Witten, and Branislav Jurco for correspondence, to Mark Doyle for sharing his Ph.D. Thesis with me, to Imperial College for support, and especially Arkady Tseytlin and the TIFR, Mumbai String Theory group, for numerous insightful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Moving NS Punctures on Super Spheres Article published earlier |
| spellingShingle | Moving NS Punctures on Super Spheres Skliros, Dimitri P. |
| title | Moving NS Punctures on Super Spheres |
| title_full | Moving NS Punctures on Super Spheres |
| title_fullStr | Moving NS Punctures on Super Spheres |
| title_full_unstemmed | Moving NS Punctures on Super Spheres |
| title_short | Moving NS Punctures on Super Spheres |
| title_sort | moving ns punctures on super spheres |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212605 |
| work_keys_str_mv | AT sklirosdimitrip movingnspuncturesonsuperspheres |