On c-theorems in arbitrary dimensions

Understand

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 CFTs.