Extended matter coupled to BF theory
Open accessAbstract
Recently, a topological field theory of membrane matter coupled to BF theory in arbitrary spacetime dimensions was proposed [J. C. Baez and A. Perez, Adv. Theor. Math. Phys. 11, 3 (2007).]. In this paper, we discuss various aspects of the four-dimensional theory. First, we study classical solutions leading to an interpretation of the theory in terms of strings propagating on a flat spacetime. We also show that the general classical solutions of the theory are in one-to-one correspondence with solutions of Einstein's equations in the presence of distributional matter (cosmic strings). Second, we quantize the theory and present, in particular, a prescription to regularize the physical inner product of the canonical theory. We show how the resulting transition amplitudes are dual to evaluations of Feynman diagrams coupled to three-dimensional quantum gravity. Finally, we remove the regulator by proving the topological invariance of the transition amplitudes.
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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 [175]
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References 38 · Cited by 25
- Authors
- Fairbairn, W. J., & Perez, A.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2008-07-08
- Volume
- 78
- Issue
- 2
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2084098117
- Cited by
- 25
- References
- 38
- Citations by year
- 2020: 1 · 2019: 1 · 2017: 2 · 2015: 1 · 2014: 1 · 2013: 3 · 2012: 5
- FWCI
- 1.78
- 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 AMU (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- BF theory, topological field theory, cosmic strings, classical solutions, Einstein field equations, canonical quantization, transition amplitudes, Feynman diagrams, three-dimensional quantum gravity, topological invariance, four-dimensional gravity
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