RG flows in d dimensions, the dilaton effective action, and the a-theorem

Understand

Motivated by the recent dilaton-based proof of the 4d a-theorem, we study the dilaton effective action for RG flows in d dimensions.

• When d is even, the action consists of a Wess-Zumino (WZ) term, whose Weyl-variation encodes the trace-anomaly, plus all Weyl-invariants.
• For d odd, the action consists of Weyl-invariants only.
• We present explicit results for the flat-space limit of the dilaton effective action in d-dimensions up to and including 8-derivative terms.