Emergence of Gravity and RG Flow
01 Jan 2017-Vol. 187, pp 283-302
TL;DR: In this paper, Padmanabhan et al. reformulated Einstein's equations in AdS as a non-perturbative RG flow that further leads to a new approach towards constructing strongly interacting QFTs.
Abstract: This is a tribute to Padmanabhan’s works on the holographic principle which have consistently enunciated the profound philosophy that the classical equations of gravity themselves hold the key to understanding their holographic origin. I discuss how this can be realised by reformulating Einstein’s equations in AdS as a non-perturbative RG flow that further leads to a new approach towards constructing strongly interacting QFTs. For a concrete demonstration, I focus on the hydrodynamic limit in which case this RG flow connects the AdS/CFT correspondence with the membrane paradigm.
Citations
More filters
TL;DR: In this paper, the authors present a collection of notes based on lectures given at IIT Madras in September 2019 and at IFT Madrid in November 2019 on applied holography and especially the analytic and numerical techniques involved.
Abstract: This is a collection of notes based on lectures given at IIT Madras in September 2019 and at IFT Madrid in November 2019. It is supposed to be a concise (and therefore not comprehensive) and pragmatic course on applied holography and especially the (basic) analytic and numerical techniques involved. The lectures are not focused on the large theoretical and fundamental background which can be found already in several places in the literature, but rather on concrete applications of Bottom-Up AdS-CFT to Hydrodynamics, QCD and Condensed Matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details of the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during my research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by himself/herself more advanced techniques and to produce independent and novel research on the topic.
81 citations
References
More filters
TL;DR: The Golden Oldie as discussed by the authors is an unretouched version of the Witten formulation of General Relativity, originally published as Chap. 7, pp. 227-264, in Gravitation: an introduction to current research, L. Witten, ed.
Abstract: This article—summarizing the authors’ then novel formulation of General Relativity—appeared as Chap. 7, pp. 227–264, in Gravitation: an introduction to current research, L. Witten, ed. (Wiley, New York, 1962), now long out of print. Intentionally unretouched, this republication as Golden Oldie is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed–but not section nor equation numbering, etc. Current institutional affiliations are encoded in: arnowitt@physics.tamu.edu, deser@brandeis.edu, misner@umd.edu.
2,050 citations
TL;DR: The holographic principle as mentioned in this paper asserts that the fundamental degrees of freedom involved in a unified description of spacetime and matter must be manifest in an underlying quantum theory of gravity, and it has yet to be explained.
Abstract: There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at $1.4\ifmmode\times\else\texttimes\fi{}{10}^{69}$ bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.
1,706 citations
TL;DR: In this article, the authors derived the shear viscosity of the finite-temperature N = 4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane.
Abstract: Using the anti–de Sitter/conformal field theory correspondence, we relate the shear viscosity ? of the finite-temperature N = 4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find ? = ? / 8N2T3. We conjecture that for finite ’t Hooft coupling gYM2N the shear viscosity is ? = f(gYM2N)N2T3, where f(x) is a monotonic function that decreases from O(x-2ln-1(1/x)) at small x to ?/8 when x??.
1,621 citations
TL;DR: In this article, a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the Hooft coupling g_s M is large, was proposed.
Abstract: We revisit the singular IIB supergravity solution describing M fractional 3-branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant \NN=1 SUSY SU(N+M)xSU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N -> N-M. Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the `t Hooft coupling g_s M is large. In the UV it approaches that of hep-th/0002159, incorporating the logarithmic flow of couplings. In the IR the deformation of the conifold gives a geometrical realization of chiral symmetry breaking and confinement. We suggest that pure \NN=1 Yang-Mills may be dual to strings propagating at small g_s M on a warped deformed conifold. We note also that the standard model itself may lie at the base of a duality cascade.
1,376 citations
TL;DR: In this article, a derivation of the nonlinear equations of boundary fluid dynamics from gravity from gravity is presented, with specific values for fluid parameters, and an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.
Abstract: Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields—arbitrary functions of the coordinates on the boundary of AdS5—we use Einstein's equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.
1,361 citations