The holographic dilaton

Abstract

We study a set of examples of holographic duals to theories with spontaneous breaking of conformal invariance in different dimensions. The geometries are domain walls interpolating between two AdS spaces, with a non-trivial background scalar field dual to a relevant operator. We comment on a subtlety in the low momentum expansion pointed out in arXiv:1304.3051 for the case of background gravity and revise the dynamical gravity results of arXiv:1207.0006, where the dilaton pole was missing in the scalar-scalar and tensor-tensor two-point functions. We compute the energy-momentum tensor and scalar two-point functions and show that there is indeed a massless dilaton pole.Comment: 28 pages. v2: references added. v3: published version in JHE

An effective theory for holographic RG flows

“…Thus our approach may be viewed as intermediate between a general conformal symmetry analysis [5][6][7][8][9] and the study of particular holographic examples (see [10] for a review and many older references e.g. [11], and also the recent work [12][13][14][15]) for the study of the low-energy τ action. We will be able to determine universal properties of this action by constructing a bulk π action and solving the equations of motion for π.…”

“…Since the O n 's are relevant operators in the UV CFT, W QFT will be independent of τ at sufficiently short distances. Thus the generating function W QFT must take the form 13) in the UV limit, where the momenta k are much larger than the scales associated with the relevant operators, so that…”

“…In the usual top-down approach to the study of holographic RG flows [10,12,13,15,[25][26][27][28], one needs to specify the bulk action and then solve the background equations of motions for the matter fields and the geometry. The obvious drawbacks of such an approach are that we lack a general rule for what types of potentials and interactions to use in order to generate an RG flow for the boundary theory, and that for given holographic RG models, the process of finding background profiles can be computationally cumbersome.…”

“…After some straightforward computations, we find that the low energy dilaton action (for modes with momenta k z −1 2 ) is given by 13) JHEP02 (2015)056 where in the second equality we have used the fact that…”

On the matching method and the Goldstone theorem in holography

“…Since then such a behavior has been re-derived on several occasions, for example in [17], where we considered a piece-wise quadratic potential in order to allow analytic treatment. In spite of the generality of the argument, the conclusion has been put into question recently in [18], where a 1/q 2ν IR propagator with ν IR > d/2 has been explicitly found in the q → 0 limit. The presence of this term is expected: it is an unavoidable part of the continuous spectrum.…”