Perturbative quantization of Yang-Mills theory with classical double as gauge algebra.

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Google Scholar
Research Projects
Organizational Units
Journal Issue
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
© The Author(s) 2016. © Springer International Publishing AG. This work was partially funded by the Spanish Ministry of Economy and Competitiveness through Grant FPA2014- 54154-P and by the European Union Cost Program through Grant MP 1405.
Unesco subjects
1. A. Achúcarro, P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories. Phys. Lett. B 180, 89 (1986)ADSMathSciNetCrossRef 2. E. Witten, (2+1)-Dimensional Gravity as an Exactly Soluble System. Nucl. Phys. B 311, 46 (1988)ADSMathSciNetCrossRefMATH 3. G. Barnich, B. Oblak, Notes on the BMS group in three dimensions: I. Induced representations. JHEP 1406, 129 (2014). arXiv:1403.5803 [hep-th] 4. G. Barnich, B. Oblak, Notes on the BMS group in three dimensions: II. Coadjoint representation, JHEP 1503, 033 (2015). arXiv:1502.00010 [hep-th] 5. G. Barnich, C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited. Phys. Rev. Lett. 105, 111103 (2010). arXiv:0909.2617 [gr-qc] 6. M. Hatsuda, K. Kamimura, W. Siegel, Type II chiral affine Lie algebras and string actions in doubled space. JHEP 1509, 113 (2015). arXiv:1507.03061 [hep-th] 7. R.F. Dashen, E.E. Jenkins, A.V. Manohar, The 1, N(c) expansion for baryons, Phys. Rev. D 49, 4713, erratum Phys. Rev. D 51(1995), 2489 (1994). arXiv:hep-ph/9310379 8. C.R. Nappi, E. Witten, A WZW model based on a nonsemisimple group. Phys. Rev. Lett. 71, 3751 (1993). arXiv:hep-th/9310112 9. K. Sfetsos, Exact string backgrounds from WZW models based on nonsemisimple groups. Int. J. Mod. Phys. A 9, 4759 (1994). arXiv:hep-th/9311093 10. K. Sfetsos, Gauging a nonsemisimple WZW model. Phys. Lett. B 324, 335 (1994). arXiv:hep-th/9311010 11. K. Sfetsos, Gauged WZW models and nonAbelian duality. Phys. Rev. D 50, 2784 (1994). arXiv:hep-th/9402031 12. N. Mohammedi, On bosonic and supersymmetric current algebras for nonsemisimple groups. Phys. Lett. B 325, 371 (1994). arXiv:hep-th/9312182 13. J.M. Figueroa-O’Farrill, S. Stanciu, Nonreductive WZW models and their CFTs. Nucl. Phys. B 458, 137 (1996). arXiv:hep-th/9506151 14. J.M. Figueroa-O’Farrill, S. Stanciu, Nonsemisimple Sugawara constructions. Phys. Lett. B 327, 40 (1994). arXiv:hep-th/9402035 15. A.A. Tseytlin, On gauge theories for nonsemisimple groups. Nucl. Phys. B 450, 231 (1995). arXiv:hep-th/9505129 16. F. Ruiz Ruiz, YangMills theory for semidirect products G ⋉g^∗and its instantons. Eur. Phys. J. C 75, 317 (2015). arXiv:1408.1049 [hep-th] 17. A. Medina, Ph Revoy, Algèbres de Lie et produit scalaire invariant. Ann. Scient. Éc. Norm. Sup. 18, 553 (1985).