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arXiv · 1711.09236

Commutative/Non-Commutative Dualities

FG Scholtz·PH Williams·JN Kriel
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Abstract

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

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FG Scholtz, PH Williams, JN Kriel. 2017-11-25. Commutative/Non-Commutative Dualities. https://arxiv.org/abs/1711.09236

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