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Dual projection and self-duality in three dimensions
Phys. Rev. D 63, 045005 – Published 18 January, 2001
DOI: https://doi.org/10.1103/PhysRevD.63.045005
Abstract
We discuss the notion of duality and self-duality in the context of the dual projection operation that creates an internal space of potentials. Distinctly from the algebraic or group theoretical methods, this technique is applicable to both even and odd dimensions. The parity in the kernel of the Gauss law is shown to play a crucial role in determining the dimensional dependence of the duality groups and actions. Using this novel concept, we derive the appropriate invariant actions and discuss the symmetry groups and their proper generators. In particular, the presence of a duality symmetry and self-duality in Maxwell theory in 2+1 dimensions is analyzed in details. The corresponding action is a 3D version of the familiar duality symmetric electromagnetic theory in 4D. Finally, the duality symmetric actions in the different dimensions constructed here manifest both the SO(2) and symmetries, contrary to conventional results.
References (9)
- P. Pasti, D. Sorokin, and M. Tonin, Phys. Lett. B 352, 59 (1995); Phys. Rev. D 52, R4277 (1995); S. Deser, Lectures given at 7th Mexican School of Particles and Fields and 1st Latin American Symposium on High-Energy Physics, Merida, Yucatan, Mexico, 1996, hep-th/9701157; D. I. Olive, in Duality and Supersymmetric Theories, edited by D. I. Olive and P. C. West (Cambridge University Press, Cambridge, England, 1997), pp. 62–94.
- C. Gomez and R. Hernandez, Lectures given at Advanced School on Effective Theories, Almunecar, Spain, 1995, hep-th/9510023; L. Alvarez-Gaume and S. F. Hassan, Fortsch. Phys. 45, 159 (1997); L. Alvarez-Gaume and F. Zamora, Duality in Quantum Field Theory and String Theory, Lectures given at CERN-La Plata-Santiago de Compostela School of Physics, 1997, hep-th/9709180; D. I. Olive, Nucl. Phys. B (Proc. Suppl.) 58, 43 (1997).
- J. Schwarz, Lectures on superstring and M theory dualities, Nucl. Phys. B (Proc. Suppl.) 55B, 1 (1997); Elias Kiritsis, Lectures given at NATO Advanced Study Institute: TMR Summer School on Progress in String Theory and M-Theory, Cargese, hep-ph/9911525.
- S. Deser, A. Gomberoff, M. Henneaux, and C. Teitelboim, Phys. Lett. B 400, 80 (1997).
- D. Zwanziger, Phys. Rev. D 3, 880 (1971); ibid.S. Deser and C. Teitelboim, 13, 1592 (1976); J. Schwarz and A. Sen, Nucl. Phys. B411, 35 (1994).
- R. Banerjee and C. Wotzasek, Nucl. Phys. B527, 402 (1998).
- R. Banerjee and Subir Ghosh, Phys. Lett. B 482, 302 (2000).
- W. Siegel, Nucl. Phys. B238, 307 (1984); R. Floreanini and R. Jackiw, Phys. Rev. Lett. 59, 1873 (1987).
- C. Wotzasek, Phys. Rev. D 58, 125026 (1998); R. Banerjee and B. Chakraborty, J. Phys. A 32, 4441 (1999).