Abstract
We use the holographic language to show the existence of the a-theorem for even dimensional CFTs, dual to the AdS space in general quadratic curvature gravity. We find the Wess-Zumino action which is originated from the spontaneous breaking of the conformal symmetry in dle 8, by using a radial cut-off near the AdS boundary. We also study the RG flow and (average) null energy condition in the space of the couplings of theory. In a simple toy model, we find the regions where this holographic RG flow has a monotonic decreasing behavior.
Highlights
In the context of two-dimensional unitary conformal field theories, the Zomolodchikov’s c-theorem [1,2] states that the central charge monotonically decreases along the Renormalization Group (RG) flow
We need the GH terms and counter-terms corresponding to the bulk action of (2.3)
The GH terms for Einstein–Hilbert and Gauss–Bonnet terms are known but with the standard method of variation, one cannot find a proper GH term for general quadratic curvature terms. We do this by computing the effective GH term on a maximally symmetric AdS space [38]
Summary
In the context of two-dimensional unitary conformal field theories, the Zomolodchikov’s c-theorem [1,2] states that the central charge monotonically decreases along the Renormalization Group (RG) flow. In this holographic approach, depending on which AdS throat we are dealing with, the coefficient of the effective dilaton action is equal to the value of aU V or aI R These AdS solutions correspond to the UV/IR fixed points of the RG flow. Unlike the four dimensional holographic CFT dual to the AdS solution in the Einstein gravity, in quasi-topological theories a = c In these theories, it is possible to show that for a general RG flow there is a monotonically decreasing function a(r ), assuming that the matter sector obeys the null energy condition. It is possible to show that for a general RG flow there is a monotonically decreasing function a(r ), assuming that the matter sector obeys the null energy condition This function at the fixed points reproduces correct values for aU V and aI R. We summarize our computations and discuss the results
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