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RG flows in d dimensions, the dilaton effective action, and the a-theorem | | Henriette Elvang
; Timothy M. Olson
; | | Date: |
15 Sep 2012 | | Abstract: | 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. GJMS-operators from conformal geometry motivate a form of the action
that unifies the Weyl-invariants and anomaly-terms into a compact general-d
structure.
A new feature in 8d is the presence of an 8-derivative Weyl-invariant that
pollutes the O(p^8)-contribution from the WZ action to the dilaton scattering
amplitudes; this may challenge a dilaton-based proof of an a-theorem in 8d.
We use the example of a free massive scalar for two purposes: 1) it allows us
to confirm the structure of the d-dimensional dilaton effective action
explicitly; we carry out this check for d=3,4,5,...,10; and 2) in 8d we
demonstrate how the flow (a_UV - a_IR) can be extracted systematically from the
O(p^8)-amplitudes despite the contamination from the 8-derivative
Weyl-invariant. This computation gives a value for the a-anomaly of the 8d free
conformal scalar that is shown to match the value obtained from zeta-function
regularization of the log-term in the free energy. | | Source: | arXiv, 1209.3424 | | Services: | Forum | Review | PDF | Favorites | |
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