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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.08101 |
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Table of Contents:
- In this paper, we introduce a new method for constructing gauged $σ$-models from four-dimensional Chern-Simons (4d CS) gauge theory. We begin with a review of recent work by several authors on the classical generation of integrable $σ$-models from 4d CS. In this approach, a gauge field is required to satisfy certain boundary conditions on two-dimensional defects inserted into the bulk. Using these boundary conditions, the equations of motion are solved, and the result is substituted back into the action. This yields a $σ$-model whose integrability is guaranteed because the 4d CS field is gauge equivalent to a Lax connection. Using a theory consisting of two 4d CS fields coupled together on new classes of ``gauged'' defects, we construct gauged $σ$-models and identify a unifying action. These models are conjectured to be integrable because the 4d CS fields remain gauge equivalent to two Lax connections. Finally, we consider two examples: the gauged Wess-Zumino-Witten model and the nilpotent gauged Wess-Zumino-Witten models. This latter model is of note as one can find the conformal Toda models from it.