Two-dimensional topological field theories coupled to four-dimensional BF theory
Open accessAbstract
Four-dimensional BF theory admits a natural coupling to extended sources supported on two-dimensional surfaces or string world sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two-dimensional world sheet. We show how two-dimensional Yang-Mills degrees of freedom can be added on the world sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two-dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background-independent quantum field theory where local degrees of freedom at low energies arise from global topological (world sheet) degrees of freedom at the fundamental level.
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In four-dimensional BF theory, topological defects are string-like and can carry extra degrees of freedom such as topological Yang-Mills fields.
“In the four-dimensional case, defects are string-like [175] and can carry extra degrees of freedom such as topological Yang-Mills fields [275].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [275]
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- Authors
- Montesinos, M., & Perez, A.
- Affiliations
- Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (MX)
- ORCID
- Montesinos, Merced
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2008-05-19
- Volume
- 77
- Issue
- 10
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2594271103
- Cited by
- 13
- References
- 40
- Citations by year
- 2016: 1 · 2013: 1 · 2012: 3
- FWCI
- 1.43
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- topological field theory, BF theory, two-dimensional Yang-Mills theory, worldsheet, cosmic strings, Einstein field equations, tetrads, background-independent quantum gravity, exact quantization, string worldsheet
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