M-Theory with Framed Corners and Tertiary Index Invariants
The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146824 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | M-Theory with Framed Corners and Tertiary Index Invariants / H. Sati // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 87 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718867608961024 |
|---|---|
| author | Sati, H. |
| author_facet | Sati, H. |
| citation_txt | M-Theory with Framed Corners and Tertiary Index Invariants / H. Sati // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 87 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams e-invariant. If the eleven-dimensional manifold itself has a boundary, the resulting ten-dimensional manifold can be viewed as a codimension two corner. The partition function in this context has been studied by the author in relation to index theory for manifolds with corners, essentially on the product of two intervals. In this paper, we focus on the case of framed manifolds (which are automatically Spin) and provide a formulation of the refined partition function using a tertiary index invariant, namely the f-invariant introduced by Laures within elliptic cohomology. We describe the context globally, connecting the various spaces and theories around M-theory, and providing a physical realization and interpretation of some ingredients appearing in the constructions due to Bunke-Naumann and Bodecker. The formulation leads to a natural interpretation of anomalies using corners and uncovers some resulting constraints in the heterotic corner. The analysis for type IIA leads to a physical identification of various components of eta-forms appearing in the formula for the phase of the partition function.
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| first_indexed | 2025-12-07T18:17:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146824 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:17:49Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sati, H. 2019-02-11T16:34:05Z 2019-02-11T16:34:05Z 2014 M-Theory with Framed Corners and Tertiary Index Invariants / H. Sati // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 87 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T50; 55N20; 58J26; 58J22; 58J28; 81T30 DOI:10.3842/SIGMA.2014.024 https://nasplib.isofts.kiev.ua/handle/123456789/146824 The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams e-invariant. If the eleven-dimensional manifold itself has a boundary, the resulting ten-dimensional manifold can be viewed as a codimension two corner. The partition function in this context has been studied by the author in relation to index theory for manifolds with corners, essentially on the product of two intervals. In this paper, we focus on the case of framed manifolds (which are automatically Spin) and provide a formulation of the refined partition function using a tertiary index invariant, namely the f-invariant introduced by Laures within elliptic cohomology. We describe the context globally, connecting the various spaces and theories around M-theory, and providing a physical realization and interpretation of some ingredients appearing in the constructions due to Bunke-Naumann and Bodecker. The formulation leads to a natural interpretation of anomalies using corners and uncovers some resulting constraints in the heterotic corner. The analysis for type IIA leads to a physical identification of various components of eta-forms appearing in the formula for the phase of the partition function. The author thanks Ulrich Bunke for explaining his work and Niranjan Ramachandran for discussions
 on divided congruences. This research is supported by NSF Grant PHY-1102218. The
 author is indebted to the anonymous referees for many corrections and helpful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications M-Theory with Framed Corners and Tertiary Index Invariants Article published earlier |
| spellingShingle | M-Theory with Framed Corners and Tertiary Index Invariants Sati, H. |
| title | M-Theory with Framed Corners and Tertiary Index Invariants |
| title_full | M-Theory with Framed Corners and Tertiary Index Invariants |
| title_fullStr | M-Theory with Framed Corners and Tertiary Index Invariants |
| title_full_unstemmed | M-Theory with Framed Corners and Tertiary Index Invariants |
| title_short | M-Theory with Framed Corners and Tertiary Index Invariants |
| title_sort | m-theory with framed corners and tertiary index invariants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146824 |
| work_keys_str_mv | AT satih mtheorywithframedcornersandtertiaryindexinvariants |