Matroid Theory and Chern-Simons

Abstract

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 D=11 supergravity. Our approach also seems to be related to loop solutions of quantum gravity based in Ashtekar formalism.

18 pages, Latex

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• Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity
• Search for a "Gravitoid" Theory
• Soldered Bundle Background for the De Sitter Top
• Superfield Description of a Self-Dual Supergravity a la MacDowell-Mansouri
• Towards an Ashtekar Formalism in Twelve Dimensions
• Hamiltonian Noether theorem for gauge systems and two time physics
• Generalized Elko Theory
• Some Mathematical and Physical Remarks on Surreal Numbers
• Thoughts on Duality and Fundamental Constants