Holographic Renormalization
By M. Bianchi, D. Freedman, Kostas Skenderis. 2001
706 citations recorded by the source corpus.
We systematically develop the procedure of holographic renormalization for RG flows dual to asymptotically AdS domain walls. All divergences of the on-shell bulk action can be cancelled by adding covariant local boundary counterterms determined by the near-boundary behavior of bulk fields. This procedure defines a renormalized action from which correlation functions are obtained by functional differentiation. The correlators are finite and well behaved at coincident points. Ward identities, corrected for anomalies, are satisfied. The correlators depend on parts of the solution of the bulk field equations which are not determined by near-boundary analysis. In principle a full nonlinear solution is required, but one can solve linearized fluctuation equations to define a bulk-to-boundary propagator from which 2-point correlation functions are easily obtained. We carry out the procedure explicitly for two known RG flows obtained from the maximal gauged D=5 supergravity theory, obtaining new results on correlators of vector currents and related scalar operators and giving further details on a recent analysis of the stress tensor sector. 1 M.Bianchi@damtp.cam.ac.uk 2 dzf@math.mit.edu kostas@feynman.princeton.edu
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/02312d61a1b66fe59bfccb1a083bbcc7828205f6
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Citations in the corpus
- Holography and thermodynamics of 5D dilaton-gravity (2008, background): “sure that (vacuum and black-hole) solutions that extend to arbitrarily large values of λexist. – 24 – The counterterm action Sǫ count is required to make the above expression finite in the limit ǫ → 0 [45]. As we can see, eq. (3.17) depends solely on the metric evaluated at the UV cutoff: the contribu”
- Fuzzballs with internal excitations (2007, methodology): “A systematic method for extracting vevs from asymptotically AdS ×X solutions (with X an arbitrary compact manifold) was only recently constructed, in [10], building on earlier work [24, 25, 26, 27, 28], see also the review [29].”
- Gravitation from entanglement in holographic CFTs (2013, background): “Of course, this expression is the usual result for the linearized holographic stress tensor in Einstein gravity in AdSd+1 [40–44].”
- Lectures on gauged supergravity and flux compactifications (2008, background): “SYM boundary theory, such as holographic RG flows and the anomalous conformal dimensions of operators [20, 21, 22].”
- Thermodynamics and instabilities of a strongly coupled anisotropic plasma (2011, positive): “Holographic renormalization for supergravity solutions dual to field theory RG flows was initiated in [104, 105].”
- The fuzzball proposal for black holes (2008, background): “Higher point functions can be obtained by solving the fluctuation equations around the original solution [31, 32, 33, 34] but this will not be reviewed here.”
- Bulk viscosity of strongly coupled plasmas with holographic duals (2008, background): “This is not to say that G cannot be determined: it is closely related to counterterms in the prescription for computing Green’s functions which are widely studied: see for example [17, 18, 19].”
- Correlation functions in holographic RG flows (2004, methodology): “This also agrees with the results in [4, 5].”
- Holography at finite cutoff with a T2 deformation (2018, methodology): “Most of the work on this topic has focused on understanding the long distance physics of the original CFT, in the spirit of the renormalization group [2–7].”
- Adding flavor to AdS/CFT (2002, result): “A very similar result was obtained in [18, 19] where it was also found that the definition of the subleading term in the presence of the leading term requires a more careful treatment.”
- Branes in AdS and pp-wave spacetimes (2002, methodology): “To properly compute correlation functions one would need to implement the program of holographic renormalization [63, 64, 65] in the current setting.”
- Hydrodynamics of R-charged black holes (2006, background): “osity η = π 8 N2T3 0 p (1+κ1)(1+κ2)(1+κ3) = πN2T3 H Q3 i=1 (1+κi)2 (2+κ1 +κ2 +κ3 − κ1κ2κ3)3 . (3.11) 4For a discussion of relevant issues in the context of holographic renormalization, see e.g. [17], [18], [19], [20], [21]. – 7 – Comparing this result with the expression (2.9) for the entropy densit”