Higher gauge theory and M-theory
In this thesis, the emerging field of higher gauge theory will be discussed, particularly in relation to problems arising in M-theory, such as selfdual strings and the so-called (2,0) theory. This thesis will begin with a Nahm-like construction for selfdual strings using loop space, the space of loo...
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| Format: | Journal article |
| Language: | English |
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Cornell University
2014
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| _version_ | 1797084912579248128 |
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| author | Palmer, S |
| author_facet | Palmer, S |
| author_sort | Palmer, S |
| collection | OXFORD |
| description | In this thesis, the emerging field of higher gauge theory will be discussed, particularly in relation to problems arising in M-theory, such as selfdual strings and the so-called (2,0) theory. This thesis will begin with a Nahm-like construction for selfdual strings using loop space, the space of loops on spacetime. This construction maps solutions of the Basu-Harvey equation, the BPS equation arising in the description of multiple M2-branes, to solutions of a selfdual string equation on loop space. Furthermore, all ingredients of the construction reduce to those of the ordinary Nahm construction when compactified on a circle with all loops restricted to those wrapping the circle. The rest of this thesis, however, will not involve loop space. We will see a Nahm-like construction for the case of infinitely many selfdual strings, suspended between two M5-branes. This is possible since the limit taken renders the fields describing the M5-branes abelian. This avoids the problem which the rest of this thesis focuses on: What fields describe multiple M5-branes? The answer is likely to involve higher gauge theory, a categorification of gauge theory which describes the parallel transport of extended objects. Any theories which involves 3-algebras, including current M2-brane models and the Lambert-Papageorgakis M5-brane model, are examples of higher gauge theories. Recently, a class of models with N=(1,0) supersymmetry have been found, with significant overlap with algebraic structures in higher gauge theory. This overlap suggests that the full N=(2,0) theory could involve semistrict L∞-algebras. Finally, we will see some explicit selfdual string solutions, which may fit into these frameworks. |
| first_indexed | 2024-03-07T02:01:49Z |
| format | Journal article |
| id | oxford-uuid:9da40237-c2c7-403a-8ef5-79be72011264 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:01:49Z |
| publishDate | 2014 |
| publisher | Cornell University |
| record_format | dspace |
| spelling | oxford-uuid:9da40237-c2c7-403a-8ef5-79be720112642022-03-27T00:44:26ZHigher gauge theory and M-theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9da40237-c2c7-403a-8ef5-79be72011264EnglishSymplectic ElementsCornell University2014Palmer, SIn this thesis, the emerging field of higher gauge theory will be discussed, particularly in relation to problems arising in M-theory, such as selfdual strings and the so-called (2,0) theory. This thesis will begin with a Nahm-like construction for selfdual strings using loop space, the space of loops on spacetime. This construction maps solutions of the Basu-Harvey equation, the BPS equation arising in the description of multiple M2-branes, to solutions of a selfdual string equation on loop space. Furthermore, all ingredients of the construction reduce to those of the ordinary Nahm construction when compactified on a circle with all loops restricted to those wrapping the circle. The rest of this thesis, however, will not involve loop space. We will see a Nahm-like construction for the case of infinitely many selfdual strings, suspended between two M5-branes. This is possible since the limit taken renders the fields describing the M5-branes abelian. This avoids the problem which the rest of this thesis focuses on: What fields describe multiple M5-branes? The answer is likely to involve higher gauge theory, a categorification of gauge theory which describes the parallel transport of extended objects. Any theories which involves 3-algebras, including current M2-brane models and the Lambert-Papageorgakis M5-brane model, are examples of higher gauge theories. Recently, a class of models with N=(1,0) supersymmetry have been found, with significant overlap with algebraic structures in higher gauge theory. This overlap suggests that the full N=(2,0) theory could involve semistrict L∞-algebras. Finally, we will see some explicit selfdual string solutions, which may fit into these frameworks. |
| spellingShingle | Palmer, S Higher gauge theory and M-theory |
| title | Higher gauge theory and M-theory |
| title_full | Higher gauge theory and M-theory |
| title_fullStr | Higher gauge theory and M-theory |
| title_full_unstemmed | Higher gauge theory and M-theory |
| title_short | Higher gauge theory and M-theory |
| title_sort | higher gauge theory and m theory |
| work_keys_str_mv | AT palmers highergaugetheoryandmtheory |