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Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly
From the holographic renormalizationg group viewpoint, while the scale
transformation plays a primary role in the duality by providing the extra
dimension, the special conformal transformation seems to only play a secondary
role. We, however, claim that the space-time diffeomorphism is crucially
related to the latter. For its demonstration, we study the holographic
renormalization group flow of a foliation preserving diffeomophic theory of
gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field
theory, if any, is only scale invariant but not conformal invariant. In
particular, we show that the holographic trace anomaly in four-dimension
predicts the Ricci scalar squared term that would be incompatible with the
Wess-Zumino consistency condition if it were conformal. This illustrates how
the foliation preserving diffeomophic theory of gravity could be inconsistent
with a theorem of the dual unitary quantum field theory.Comment: 18 pages, v2: reference added, v3: comments on more recent literature
added in response to referee's reques