Document Type : Original Article
Department of Physics, Shahid Beheshti University, 1983969411, Tehran, Iran
In this paper, we consider the massive quarks interacting with an external non-abelian gauge field (gluon) in (1+2)-dimensional spacetime. By integrating out the quark fields, we obtain the general structure of the one-loop effective action for the gluons coupled to the quarks. Next, we compute the one-loop Feynman graphs related to one, two, three and four-point functions for the gluon, by using dimensional regularization. We explicitly show that the resulting effective action, at the low-energy limit (), leads to the non-Abelian Chern-Simons and Yang-Mills action. This induced action, arising from the quantum corrections due to the fermionic loops, also respects Lorentz and gauge invariance.
- L Bonora, M Cvitan, P Dominis Prester, S Giaccari, B Lima de Souza and T temberga, JHEP 1612 (2016) 084, arXiv:1609.02088 [hep-th].
- L Bonora, M Cvitan, P Dominis Prester, S Giaccari and T temberga, JHEP 1801 (2018) 080, arXiv:1709.01738 [hep-th].
- J Quevillon, C Smith and S Touati, Rev. D 99 (2019) 1, 013003, arXiv:1810.06994 [hep-th].
- R Bufalo and M Ghasemkhani, Rev. D 91 (2015) 12, 125013, arXiv:1412.1635 [hep-th].
- M Ghasemkhani, R Bufalo , V Rahmanpour and M Alipour, Rev. D 101 (2020) 2, 025001, arXiv:1909.04941[hep-th].
- A N Redlich, Rev. Lett. 52(1984) 18.
- G Ferretti, S G Rajeev and Z Yang, J. Mod. Phys. A 7(1992) 7989.
- R Bufalo, M Ghasemkhani, Z Haghgouyan, and A Soto, "Induced Maxwell-Chern-Simons Effective Action in Very Special Relativity", submitted to Phys. J. C, arXiv:2004.02176[hep-th].
- A De Simone and T Jacques, Phys. J. C 76 (2016) 367, arXiv:1603.08002 [hep-ph] .
- C Cheung, P Creminelli, A L Fitzpatrick, J Kaplan, and L Senatore, JHEP 03 (2008) 014.
- J J M Carrasco, M P Hertzberg, and L Senatore, JHEP 09 (2012) 082, arXiv:2926[astro-ph.co].
- W Heisenberg and H Euler, Z Phys. 98 (1936) 714.
- N Seiberg and Sh-H Shao, "Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory", arXiv:2003.10466[cond-mat.str-el].
- P S Hsin and N Seiberg, JHEP 1609 (2016) 095, arXiv:1607.07457 [hep-th].
- F Benini, P S Hsin and N Seiberg, JHEP 1704 (2017) 135, arXiv:1702.07035 [cond-mat.str-el].
- S Deser and A N Redlich, Rev. Lett. 61 (1988) 1541.
- M E Peskin, D V Schroeder, "An Introduction to Quantum Field Theory", Addison-Wesley (1995).