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arXiv · 2108.06426

Dualities and models in various dimensions

Enrique F. Moreno·Fidel A. Schaposnik
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Abstract

Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we arrive to the partition function of a $U(1)$ gauge theory coupled to a scalar field with an action that exhibits a Dirac monopole solution. A subsequent reduction to $d=2$ dimensions leads to the partition function of a theory in which the gauge field decouples from two scalars which have non-trivial vortex-like solutions. Finally this $d=2$ partition function can be related to the bosonized version of the two-dimensional QED$_2$ (Schwinger) model.

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Enrique F. Moreno, Fidel A. Schaposnik. 2021-08-13. Dualities and models in various dimensions. https://doi.org/10.1016/j.physletb.2021.136620

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