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High Energy Physics - Theory

arXiv:1503.01424 (hep-th)
[Submitted on 4 Mar 2015]

Title:Extending dualities to trialities deepens the foundations of dynamics

Authors:Lee Smolin
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Abstract:Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables.
To illustrate this, we study matrix models with a cubic action, and show how breaking its natural triality symmetry by imposing different compactifications yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.
Comments: Latex, 12 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1503.01424 [hep-th]
  (or arXiv:1503.01424v1 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.1503.01424
Related DOI: https://doi.org/10.1007/s10773-016-3168-7

Submission history

From: Lee Smolin [view email]
[v1] Wed, 4 Mar 2015 19:16:22 UTC (10 KB)
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