Abstract
We propose a generalization of Chern–Simons (CS) modified gravity in first-order formalism. CS modified gravity action has a term that comes from the chiral anomaly which is Pontryagin invariant. First-order CS modified gravity is a torsional theory and in a space-time with torsion the chiral anomaly includes a torsional topological term called Nieh-Yan invariant. We generalize the CS modified gravity by adding the Nieh-Yan term to the action and find the effective theory. We compare the generalized theory with the first-order CS modified gravity and comment on the similarities and differences.
Similar content being viewed by others
References
Deser, S., Duff, M.J., Isham, C.J.: Phys. Lett. 93B, 419 (1980)
Freidel, L., Minic, D., Takeuchi, T.: Phys. Rev. D 72, 104002 (2005)
Ashtekar, A.: In: Lectures on Non-perturbative Canonical Gravity. Notes Prepared in Collaboration with R. S. Tate, World Scientific, Singapore (1991)
Holst, S.: Phys. Rev. D 53, 5966 (1996)
Immirzi, G.: Class. Quant. Gravit. 14, L177 (1997)
Fatibene, L., Ferraris, M., Francaviglia, M.: Class. Quant. Gravit. 27, 165021 (2010)
Jackiw, R., Pi, S.-Y.: Phys. Rev. D 68, 104012 (2003)
Alexander, S., Yunes, N.: Chern–Simons Modified General Relativity. arXiv:0907.2562[hep-th]
Grumiller, D., Mann, R., McNees, R.: Phys. Rev. D 78, 081502 (2008)
Smith, T.L., Erickcek, A.L., Caldwell, R.R., Kamionkowski, M.: Phys. Rev. D 77, 024015 (2008)
Konno, K., Matsuyama, T., Asano, Y., Tanda, S.: Phys. Rev. D 78, 024037 (2008)
Yunes, N., Pretorius, F.: Phys. Rev. D 79, 084043 (2009)
Cantcheff, M.B.: Phys. Rev. D 78, 025002 (2008)
Alexander, S., Yunes, N.: Phys. Rev. D 77, 124040 (2008)
Nieh, H.T., Yan, M.L.: J. Math. Phys. 23, 373 (1982)
Chandia, O., Zanelli, J.: Torsional Topological Invariants (and their relevance for real life). arXiv:hep-th/9708138
Hehl, F.W., McCrea, J.D., Mielke, E.W., Ne’eman, Y.: Phys. Rep. 258, 1 (1995)
Alexander, S.H.S., Gates, S.J. Jr.: JCAP 0606, 018 (2006)
Chandia, O., Zanelli, J.: Phys. Rev. D 55, 7580 (1997)
Soo, C.: Phys. Rev. D 59, 045006 (1999)
Li, S.: J. Phys. A 32, 7153 (1999)
Mielke, E.W.: AIP Conf. Proc. 857B, 246 (2006)
Mercuri, S.: Phys. Rev. Lett. 103, 081302 (2009)
Mercuri, S., Taveras, V.: Phys. Rev. D 80, 104007 (2009)
Taveras, V., Yunes, N.: Phys. Rev. D 78, 064070 (2008)
Torres-Gomez, A., Krasnov, K.: Phys. Rev. D 79, 104014 (2009)
Lattanzi, M., Mercuri, S.: Phys. Rev. D 81, 125015 (2010)
MacDowell, S.W., Mansouri, F.: Phys. Rev. Lett. 38, 739 (1977), ibid. 38, 1376 (1977)
Calcagni, G., Mercuri, S.: Phys. Rev. D 79, 084004 (2009)
Acknowledgments
This work was supported in part by the Scientific and Technical Research Council of Turkey (TÜBİTAK).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ertem, Ü., Açık, Ö. Generalized Chern–Simons modified gravity in first-order formalism. Gen Relativ Gravit 45, 477–488 (2013). https://doi.org/10.1007/s10714-012-1483-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10714-012-1483-8