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arXiv · 2405.09473

Some Lower Dimensional Quantum Field Theories Reduced from Chern-Simons Gauge Theories

Burak Oğuz·Bayram Tekin
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Abstract

We study symmetry reductions in the context of Euclidean Chern-Simons gauge theories to obtain lower dimensional field theories. Symmetry reduction in certain gauge theories is a common tool for obtaining explicit soliton solutions. Although pure Chern-Simons theories do not admit solitonic solutions, symmetry reduction still leads to interesting results. We establish relations at the semiclassical regime between pure Chern-Simons theories on $S^3$ and the reduced Quantum Field Theories, based on actions obtained by the symmetry reduction of the Chern-Simons action, spherical symmetry being the prominent one. We also discuss symmetry reductions of Chern-Simons theories on the disk, yielding $BF$-theory in two dimensions, which signals a curious relationship between symmetry reductions and the boundary conformal field theories. Finally, we study the Chern-Simons-Higgs instantons and show that under certain circumstances, the reduced action can formally be viewed as the action of a supersymmetric quantum mechanical model. We discuss the extent to which the reduced actions have a fermionic nature at the level of the partition function.

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Burak Oğuz, Bayram Tekin. 2024-05-15. Some Lower Dimensional Quantum Field Theories Reduced from Chern-Simons Gauge Theories. https://doi.org/10.1103/physrevd.110.085019

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