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c-theorems in arbitrary dimensions

Bhattacharyya, Arpan and Hung, Ling-Yan and Sen, Kallol and Sinha, Aninda (2012) c-theorems in arbitrary dimensions. In: PHYSICAL REVIEW D, 86 (10).

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Official URL: http://dx.doi.org/10.1103/PhysRevD.86.106006


The dilaton action in 3 + 1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the trace anomaly. Since there are no anomalies in odd dimensions, it is interesting to ask how such an action could arise otherwise. Motivated by this we use the AdS/CFT correspondence to examine both even and odd dimensional conformal field theories. We find that in even dimensions, by promoting the cutoff to a field, one can get an action for this field which coincides with the Wess-Zumino action in flat space. In three dimensions, we observe that by finding an exact Hamilton-Jacobi counterterm, one can find a non-polynomial action which is invariant under global Weyl rescalings. We comment on how this finding is tied up with the F-theorem conjectures.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to AMER PHYSICAL SOC, USA
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 19 Dec 2012 11:01
Last Modified: 19 Dec 2012 11:01
URI: http://eprints.iisc.ac.in/id/eprint/45543

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