AdS/CFT correspondence and geometry

By Ioannis Papadimitriou, Kostas Skenderis. 2004

356 citations recorded by the source corpus.

In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In the second part we develop a Hamiltonian approach to the method of holographic renormalization, with the radial coordinate playing the role of time. In this approach regularized correlation functions are related to canonical momenta and the near-boundary expansions of the standard approach are replaced by covariant expansions where the various terms are organized according to their dilatation weight. This leads to universal expressions for counterterms and one-point functions (in the presence of sources) that are valid in all dimensions. The new approach combines optimally elements from all previous methods and supersedes them in efficiency.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a4ab3a26c40c4d324c11aec7387415ee70618456

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. V. Hubeny
2. M. Rangamani
3. R. Myers
4. Marika Taylor
5. S. Hartnoll
6. T. Takayanagi
7. J. Maldacena
8. D. Harlow

In Nuclear and High Energy Physics

1. M. Rangamani
2. V. Hubeny
3. R. Myers
4. S. Hartnoll
5. T. Takayanagi
6. D. Harlow
7. J. Maldacena
8. Marika Taylor

Citations in the corpus

• Thermodynamics of Asymptotically Locally AdS Spacetimes (2005, background): “3.1 The theory 6 3.2 Asymptotic analysis 8 3.3 Gauge invariance of the renormalized action 11 3.4 Variational problem 13”
• Real-time gauge/gravity duality: prescription, renormalization and examples (2008, methodology): “Alternatively, we may use the ‘radial Hamiltonian’ approach to holographic renormalization [36, 41], which provides a more efficient way of obtaining renormalized correlators.”
• 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].”
• AdS2 holographic dictionary (2016, background): “Dual operators Having determined the boundary counterterm we can now evaluate the exact renormalized one-point functions in the presence of sources which are given by the renormalized canonical momenta [66], namely T = 2π̂ t, Oψ = −π̂ψ, J t = −π̂, (3.”
• Nonlinear fluid dynamics from gravity (2007, methodology): “The Fefferman-Graham [48] method (or equivalently the formalism of holographic renormalization, see [49, 50] for reviews) demonstrates that any such conserved stress tensor, regarded as a boundary condition to Einstein’s equations, leads to a unique and well defined power series expansion (in 1/r) o”
• Real‐time response in AdS/CFT with application to spinors (2009, background): “Note that in general the limit r → ∞ in (13) is non-trivial and requires careful renormalization, which was developed systematically in [13, 14].”
• Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, methodology): “, [14, 15, 16, 17, 18, 19, 20, 21, 22, 23]) which evaluated this difference on particular solutions (e.”
• Universal hydrodynamics of non-conformal branes (2009, neutral): “The conformal conservation equation (3.2) reduces to [12] ∇iTij − ∂jκ(0)〈Oφ〉 = 0, (3.6) where 〈Oφ〉 is again the expectation value of the operator dual to φ.”
• Holographic entanglement entropy in Lovelock gravities (2011, background): “[89], the expansion may include half integral powers of ρ [90-92].”
• Kaluza-Klein Holography (2006, methodology): “Following [16] one can show that there is a one to one correspondence between the momentum coefficients and the coefficients in (5.”
• Holography for Schrödinger backgrounds (2010, methodology): “1), guarantee that all divergences are local in the boundary data [37, 38].”
• Comments on string theory backgrounds with non-relativistic conformal symmetry (2008, methodology): “We expect that the five-dimensional truncations that we derived in this paper will be important in formulating a holographic renormalisation procedure, using for instance the Hamilton-Jacobi approach [38, 39].”
• Correlation functions in holographic RG flows (2004, methodology): “Using the Gauss-Codazzi relations the bulk equations of motion are reduced to [9] K(2) −KijK = R+ κ(2) [”