It is shown that matroid theory may provide a natural mathematical framework for a duality symmetries not only for quantum Yang–Mills physics, but also for M-theory. Our discussion is focused in an action consisting purely of the Chern–Simons term, but in principle the main ideas can be applied beyond such an action. In our treatment the theorem due to Thistlethwaite, which gives a relationship between the Tutte polynomial for graphs and Jones polynomial for alternating knots and links, plays a central role. Before addressing this question we briefly mention some important aspects of matroid theory and we point out a connection between the Fano matroid and supergravity. Our approach also seems to be related to loop solutions of quantum gravity based in an Ashtekar formalism.
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December 2000
Research Article|
December 01 2000
Matroid theory and Chern–Simons
J. A. Nieto;
J. A. Nieto
Facultad de Ciencias Fı́sico-Matemáticas de la Universidad Autónoma de Sinaloa, 80010 Culiacán Sinaloa, México
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M. C. Marı́n
M. C. Marı́n
Facultad de Ciencias Fı́sico-Matemáticas de la Universidad Autónoma de Sinaloa, 80010 Culiacán Sinaloa, México
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J. Math. Phys. 41, 7997–8005 (2000)
Article history
Received:
June 01 2000
Accepted:
August 16 2000
Citation
J. A. Nieto, M. C. Marı́n; Matroid theory and Chern–Simons. J. Math. Phys. 1 December 2000; 41 (12): 7997–8005. https://doi.org/10.1063/1.1319518
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