The hierarchy of bulk actions is developed which are associated with Chern-Simons theories. The connection between the bulk and edge arising from the requirement there is a cancelation of an anomaly which arises in the theory. A duality transformation is studied for the Chern-Simons example. The idea that is used has been employed to describe duality in a scalar theory. The link between the edge theory with the Chern-Simons theory in the bulk then suggests that similar transformations can be implemented in the bulk Chern-Simons theory as well.
References
[1]
Fradkin, E. (1991) Field Theories of Condensed Matter Systems. Addison-Wesley, Reading.
[2]
Nagaosa, N. (1999) Quantum Field Theory of Condensed Matter Physics. Springer, Berlin. https://doi.org/10.1007/978-3-662-03774-4
[3]
Oh, P. (1996) Nuclear Physics B, 462, 551-570. https://doi.org/10.1016/0550-3213(95)00669-9
[4]
Balachandran, A.P., Chander, L. and Sathiapalen, B. (1995)Nuclear Physics B, 443, 465-500. https://doi.org/10.1016/0550-3213(95)00122-9
[5]
Zee, A. (1992)Progress of Theoretical Physics, Supplement, 107, 77-100. https://doi.org/10.1143/PTPS.107.77
[6]
Fröhlich, J. and Keller, T. (1991) Nuclear Physics B, 354, 369-417. https://doi.org/10.1016/0550-3213(91)90360-A
[7]
Karabali, D. and Nair, V.P. (2006) Journal of Physics A: Mathematical and General, 39, 12735-12763. https://doi.org/10.1088/0305-4470/39/41/S05
[8]
Watson, G. (1996) Contemporary Physics, 37, 127-143. https://doi.org/10.1080/00107519608230340
Balatsky, A. and Fradkin, E. (1991) Physical Review B, 43, 10622-10634.
[15]
Karabali, D. and Nair, V. (2016) Physical Review D, 94, 064057. https://doi.org/10.1103/PhysRevD.94.064057
[16]
Jotzu, G., Messer, M., Desbuquois, R., Lebrat, M., Uehlinger, T., Grief, D. and Esslinger, T. (2014) Nature, 515, 237-240. https://doi.org/10.1038/nature13915
[17]
Mandel, S. and Basu, S. (2023) Physical Review B, 107, 035421.
