Effective AdS/renormalized CFT

We propose a method for determining the exact correspondence between the Wilsonian cut-off scale on the boundary and its holographically dual bulk theory. We systematically construct the multi-trace Wilsonian effective action from holographic renormalisation and evolve it by integrating out the asymptotically Anti-de Sitter bulk geometry with scalar probes. The Wilsonian nature of the effective action is shown by proving that it must be either double-trace, closing in on itself under successive integrations, or have an infinite series of multi-trace terms. Focusing on composite scalar operator renormalisation, we relate the Callan-Symanzik equation, the flow of the scalar anomalous dimension and the multi-trace beta functions to their dual RG flows in the bulk. Establishing physical renormalisation conditions on the behaviour of the large-N anomalous dimension then enables us to extract the energy scales. Examples of pure AdS, GPPZ flow, black brane in AdS, M2 and M5 branes are studied before we generalise our results to arbitrary numbers of mass and thermal deformations of an ultra-violet CFT. Relations between the undeformed Wilsonian cut-off, deformation scales and the deformed Wilsonian cut-off are discussed, as is phenomenology of each considered background. We see how a mass gap, the emergent infra-red CFT scaling, etc. arise in different effective theories. We also argue that these results can have alternative interpretations through the flow of the conformal anomaly or the Ricci scalar curvature of boundary branes. They show consistency with the c-theorem.

Section: Introductionmentioning

confidence: 99%

Wilsonian renormalisation and the exact cut-off scale from holographic duality

Grozdanov

2012

“…All these operators have the same global quantum numbers as the simple pair operator with scaling dimension 2∆ Ψ , but increase their dimension by two integer units each time. The correlation function study [28,29] in particular shows that in the case of an interacting purely scalar bulk theory, all these linearly independent double trace primaries mix in as well and cause single-pole Feschbach resonances in s-wave scattering of single trace operators. The correspondence between the 2n difference in scaling dimension 5 between each successive primary and the location of the resonance in the leading part of the bulk scalar wavefunction supports that this mixing is the right interpretation of the resonance.…”

Section: Jhep09(2014)106mentioning

confidence: 99%

“…In AdS/CFT this connection between mixing and resonances is in fact cleanly seen in correlation functions of bilinear operators [28,29]. These bilinear operators are also known as double trace operators, since in the models where we know the dual CFT, each operator dual to an AdS field is a single trace over an N × N matrix valued combination of fields.…”

Section: A Dynamical Bcs Scalar and A Bcs/bec Crossovermentioning

confidence: 99%

“…To construct this correct set of counterterms and deduce the appropriate extraction of the vev in the boundary field theory is an interesting question to pursue. In order to make it possible we have to figure our what the set of primary operators is by diagonalizing the infinite tower of mixed operators [28,29]. It will be a subject of one of our subsequent papers.…”

Section: Jhep09(2014)106mentioning

confidence: 99%

See 1 more Smart Citation

Pairing induced superconductivity in holography

Bagrov

Meszena

Schalm

2014

We study pairing induced superconductivity in large N strongly coupled systems at finite density using holography. In the weakly coupled dual gravitational theory the mechanism is conventional BCS theory. An IR hard wall cut-off is included to ensure that we can controllably address the dynamics of a single confined Fermi surface. We address in detail the interplay between the scalar order parameter field and fermion pairing. Adding an explicitly dynamical scalar operator with the same quantum numbers as the fermion-pair, the theory experiences a BCS/BEC crossover controlled by the relative scaling dimensions. We find the novel result that this BCS/BEC crossover exposes resonances in the canonical expectation value of the scalar operator. This occurs not only when the scaling dimension is degenerate with the Cooper pair, but also with that of higher derivative paired operators. We speculate that a proper definition of the order parameter which takes mixing with these operators into account stays finite nevertheless.

“…The basic idea of hWRG is to integrate out the bulk field from the boundary up to some intermediate radial distance, yielding an equivalent dual field theory at a lower cut-off. This procedure has been exactly implemented for a free scalar field in a fixed background geometry [1,2] 1 ; see [6][7][8][9][10] for further related developments, as well as, e.g., [11][12][13][14][15][16] for earlier treatments of holographic renormalization group (the relationship between the earlier treatments and hWRG has been discussed in [1]). Although it is not easy to identify the specific dual field theories which arise in this fashion, 2 it is of interest to explore the general structure of RG flows and fixed points in these theories.…”

Section: Introductionmentioning

confidence: 99%

Holographic Wilsonian flows and emergent fermions in extremal charged black holes

Elander

Isono

Mandal

2011

We study holographic Wilsonian RG in a general class of asymptotically AdS backgrounds with a U (1) gauge field. We consider free charged Dirac fermions in such a background, and integrate them up to an intermediate radial distance, yielding an equivalent low energy dual field theory. The new ingredient, compared to scalars, involves a 'generalized' basis of coherent states which labels a particular half of the fermion components as coordinates or momenta, depending on the choice of quantization (standard or alternative). We apply this technology to explicitly compute RG flows of charged fermionic operators and their composites (double trace operators) in field theories dual to (a) pure AdS and (b) extremal charged black hole geometries. The flow diagrams and fixed points are determined explicitly. In the case of the extremal black hole, the RG flows connect two fixed points at the UV AdS boundary to two fixed points at the IR AdS 2 region. The double trace flow is shown, both numerically and analytically, to develop a pole singularity in the AdS 2 region at low frequency and near the Fermi momentum, which can be traced to the appearance of massless fermion modes on the low energy cut-off surface. The low energy field theory action we derive exactly agrees with the semi-holographic action proposed by Faulkner and Polchinski in [19]. In terms of field theory, the holographic version of Wilsonian RG leads to a quantum theory with random sources. In the extremal black hole background the random sources become 'light' in the AdS 2 region near the Fermi surface and emerge as new dynamical degrees of freedom.