Some Lower Dimensional Quantum Field Theories Reduced from Chern-Simons Gauge Theories
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 $S3$ 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.
- A. Comtet. Instantons and Minimal Surfaces. Phys. Rev. D, 18:3890, 1978.
- Gerald V. Dunne. Aspects of Chern-Simons theory. In Les Houches Summer School in Theoretical Physics, Session 69: Topological Aspects of Low-dimensional Systems, 7 1998.
- On the finite temperature Chern-Simons coefficient. Phys. Rev. Lett., 78:3434–3437, 1997.
- Monopoles in nonAbelian Chern-Simons Higgs theory. Nucl. Phys. B, 425:137–149, 1994.
- Gauge theory correlators from noncritical string theory. Phys. Lett. B, 428:105–114, 1998.
- Mirror symmetry, volume 1 of Clay mathematics monographs. AMS, Providence, USA, 2003.
- Juan Martin Maldacena. The Large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys., 2:231–252, 1998.
- N. S. Manton and P. Sutcliffe. Topological solitons. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2004.
- Richard S. Palais. The principle of symmetric criticality. Commun. Math. Phys., 69(1):19–30, 1979.
- Robert D. Pisarski. Magnetic Monopoles in Topologically Massive Gauge Theories. Phys. Rev. D, 34:3851, 1986.
- Bayram Tekin. On the relevance of singular solutions in dS(3) and AdS(3) gravity. 2 1999.
- Bayram Tekin. Multi - instantons in R**4 and minimal surfaces in R**(2,1). JHEP, 08:049, 2000.
- Complex monopoles in the Georgi-Glashow-Chern-Simons model. Nucl. Phys. B, 539:720–738, 1999.
- David Tong. Lectures on the Quantum Hall Effect. 6 2016.
- SYK Correlators from 2D Liouville-de Sitter Gravity. 2 2024.
- Edward Witten. Some Exact Multi - Instanton Solutions of Classical Yang-Mills Theory. Phys. Rev. Lett., 38:121–124, 1977.
- Edward Witten. (2+1)-Dimensional Gravity as an Exactly Soluble System. Nucl. Phys. B, 311:46, 1988.
- Edward Witten. Quantum Field Theory and the Jones Polynomial. Commun. Math. Phys., 121:351–399, 1989.
- Edward Witten. Quantization of Chern-Simons Gauge Theory With Complex Gauge Group. Commun. Math. Phys., 137:29–66, 1991.
- Edward Witten. Anti-de Sitter space and holography. Adv. Theor. Math. Phys., 2:253–291, 1998.
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