How to go with an RG flow

By M. Bianchi, D. Freedman, Kostas Skenderis. 2001

419 citations recorded by the source corpus.

We apply the formalism of holographic renormalization to domain wall solutions of 5-dimensional supergravity which are dual to deformed conformal field theories in 4 dimensions. We carefully compute one- and two-point functions of the energy-momentum tensor and the scalar operator mixing with it in two specific holographic flows, resolving previous difficulties with these correlation functions. As expected, two-point functions have a 0-mass dilaton pole for the Coulomb branch flow in which conformal symmetry is broken spontaneously but not for the flow dual to a mass deformation in which it is broken explicitly. A previous puzzle of the energy scale in the Coulomb branch flow is explained.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2181b0fb9616647ae9ae49a56adf47e98df30208

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Citations in the corpus

The holographic universe (2010, background): “The equations of motion for cosmological perturbations have been worked out long ago, see [15] and references therein, while the corresponding analysis for domain-walls may be found in [16, 17, 18].”
Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, methodology): “We therefore restrict to d ≥ 4 below, referring the reader to [ 17 ] for details of the expansion in d = 3 and saving the comparison of charges for [35].”
Entanglement entropy, trace anomalies and holography ✩ (2008, background): “This was observed and explained in [21] for conventional matter couplings to bulk gravity.”
Thermodynamics and instabilities of a strongly coupled anisotropic plasma (2011, background): “Holographic renormalization for supergravity solutions dual to field theory RG flows was initiated in [104, 105].”
Lecture notes on holographic renormalization (2002, methodology): “the fluctuations should not change if we change the representative of the conformal structure [9].”
Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields (2006, background): “(4.14) Hence, since ηr and ξm are independent, the asymptotic AdS symmetry fixes the functional relationship between a and b to be of the form (4.3) given above.”
Thermodynamics of Asymptotically Locally AdS Spacetimes (2005, methodology): “This is done for pure gravity in [18] and for gravity coupled to certain matter in [28].”
Precision holography for non-conformal branes (2008, methodology): “In the bulk, the divergences are due to the infinite volume, and are thus IR divergences, which need to be dealt with by holographic renormalization, the precise dual of standard QFT renormalization [4, 5, 6, 7, 8, 9, 10, 11]; for a review see [12].”
Holographic anatomy of fuzzballs (2006, neutral): “In this appendix we derive the 1-point function for the stress energy tensor and the operators dual to S1 i . We omit the details of this computation since the analysis is very similar to the Coulomb branch analysis in [ 41 , 42].”
Fluid dynamics of R-charged black holes (2008, methodology): “Once these are obtained, we can compute the energy momentum tensor 〈Tμν〉 and R-charged current 〈Jμ〉 of the boundary theory using the standard AdS/CFT dictionary [34, 35, 36, 37, 38, 39] adopted to Eddington-Finkelstein coordinates [18].”
Real-time gauge/gravity duality: prescription, renormalization and examples (2008, methodology): “For example, the naive computation of 2-point functions of scalar operators of scaling dimension ∆ 6= d, where the infinite terms are simply dropped, leads to results that are inconsistent with Ward identities, see [22, 23, 24, 6, 25, 26] for examples and discussions of this point.”
Heavy ions and string theory (2013, neutral): “In general, the precise calculation of the full Green’s function G requires the machinery of holographic renormalization [122, 123, 124].”