In this paper we introduce a new method for generating gauged sigma models from four-dimensional Chern-Simons theory and give a unified action for a class of these models. We begin with a review of recent work by several authors on the classical generation of integrable sigma models from four dimensional Chern-Simons theory. This approach involves introducing classes of two-dimensional defects into the bulk on which the gauge field must satisfy certain boundary conditions. One finds integrable sigma models from four-dimensional Chern-Simons theory by substituting the solutions to its equations of motion back into the action. The integrability of these sigma models is guaranteed because the gauge field is gauge equivalent to the Lax connection of the sigma model. By considering a theory with two four-dimensional Chern-Simons fields coupled together on two-dimensional surfaces in the bulk we are able to introduce new classes of 'gauged' defects. By solving the bulk equations of motion we find a unified action for a set of genus zero integrable gauged sigma models. The integrability of these models is guaranteed as the new coupling does not break the gauge equivalence of the gauge fields to their Lax connections. Finally, we consider a couple of examples in which we derive the gauged Wess-Zumino-Witten and nilpotent gauged Wess-Zumino-Witten models. This latter model is of note given one can find the conformal Toda models from it.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.