Understanding the holographic principle via RG flow

Mukhopadhyay, Ayan

doi:10.1142/s0217751x16300593

Cited by 11 publications

(16 citation statements)

References 43 publications

(95 reference statements)

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“…The proposal in [1] is that the new action would be the holographic dual to that CFT giving a concrete realisation of the AdS/CFT correspondence. 1 1 Other similar proposals include [25][26][27][28][29][30][31][32][33][34], however, this paper will restrict its attention to testing QRG.…”

Section: Iteratementioning

confidence: 99%

Developing local RG: quantum RG and BFSS

Melo

Santos

2020

J. High Energ. Phys.

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In this paper we study various forms of RG and apply these to the BFSS model of N coincident D0-branes. Firstly, as a warm-up, we perform standard Wilsonian RG, investigating the conditions under which supersymmetry is preserved along the flow. Next, we develop a local RG scheme such that the cutoff is spacetime dependent, which could have further applications to studying QFT in curved spacetime. Finally, we test the conjecture put forward in [1] that the method of quantum RG could be the mechanism responsible for the gauge/gravity duality by applying it to the BFSS model, which has a known gravitational dual. Although not entirely conclusive some questions are raised about the applicability of quantum RG as a description of the AdS/CFT correspondence.

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Section: Iteratementioning

confidence: 99%

Developing local RG: quantum RG and BFSS

Melo

Santos

2020

J. High Energ. Phys.

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“…Our biholographic construction however should not be thought of as a flow from an UV to an IR fixed point driven by a relevant deformation. 15 Rather the UV region in our case represents a strongly coupled version of usual perturbative dynamics, and the IR region represents the nonperturbative sector that exists as a shadow of the perturbative degrees of freedom in many-body quantum systems. In our case, the shadow IR theory and the hard-soft coupling constants will be determined by the parameters of the UV gravitational theory via:…”

Section: A Biholographic Illustrationmentioning

confidence: 99%

“…A natural question to ask is how we can achieve a RG flow description of the biholographic theory. The right framework is indeed a highly efficient RG flow as introduced in [13,14] (for a recent short review see [15]) which has been shown to reproduce the traditional holographic correspondence. In particular, this framework will allow us to define a conserved energy-momentum tensor of the full system at each scale without the need for introducing an action formalism.…”

Section: The Highly Efficient Rg Flow Perspectivementioning

confidence: 99%

“…Previously, semiholography has been conceived of as an effective simplified method for solving low energy holographic dynamics where the asymptotic geometry determining model-dependent features is replaced by simple boundary dynamics which couples to the near-horizon geometry controlling universal scaling exponents [4,12]. It has also been argued that decoding holography as a form of non-Wilsonian RG flow which preserves Ward identities for single-trace operators (like the energy-momentum tensor) and can selfdetermine microscopic data via appropriate infrared endpoint conditions naturally gives rise to a more general semiholographic framework in which the ultraviolet can be asymptotically free so that it is described by perturbative quantum field dynamics rather than by a classical gravity theory [13][14][15]. In this article, we will deal with the fundamental aspects of the construction of the general semiholographic framework (which may not be embeddable in string theory as we know of it today) by understanding what constrains it structurally and illustrate it with a toy example.…”

Section: Introductionmentioning

confidence: 99%

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Illustrated study of the semiholographic nonperturbative framework

2017

Self Cite

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Semiholography has been proposed as an effective nonperturbative framework which can consistently combine perturbative and nonperturbative effects for theories like QCD. It is postulated that the strongly coupled nonperturbative sector has a holographic dual in the form of a classical gravity theory in the large N limit, and the perturbative fields determine the gravitational boundary conditions. In this work, we pursue a fundamental derivation of this framework particularly showing how perturbative physics by itself can determine the holographic dual of the infrared, and also the interactions between the perturbative and the holographic sectors. We firstly demonstrate that the interactions between the two sectors can be constrained through the existence of a conserved local energy-momentum tensor for the full system up to hard-soft coupling constants. As an illustration, we set up a biholographic toy theory where both the UV and IR sectors are strongly coupled and holographic with distinct classical gravity duals. In this construction, the requirement that an appropriate gluing can cure the singularities (geodetic incompleteness) of the respective geometries leads us to determine the parameters of the IR theory and the hard-soft couplings in terms of those of the UV theory. The high energy scale behavior of the hard-soft couplings is state-independent but their runnings turn out to be state-dependent. We discuss how our approach can be adapted to the construction of the semiholographic framework for QCD.

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“…Strongly interacting theories on one side of the duality are mapped to weakly interacting theories on the other side, granting a method to perform non-perturbative computations. [39,40] Modern approaches to the holographic principle tend to view the additional dimension in the bulk quantum gravity theory as corresponding to renormalisation length scale in the boundary theory [41]. For conformal field theories this means the scale invariance of the theory would force the bulk theory to be the same regardless of how far into the bulk you moved.…”

Section: The Holographic Principlementioning

confidence: 99%

A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

McMahon¹

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Modelling strongly correlated systems is an incredibly hard problem, but a very fruitful one when achieved. The main reason for its difficulty is that perturbation theory approaches do not work for certain interesting coupling regimes. However it is believed that a holographic duality would map models with strong coupling strengths into weakly coupled bulk regimes where our current tools do work. Interest in applications to condensed matter systems has been growing throughout the past decade Though questions remain about how to do it and if the duality is valid in a relevant regime.

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Understanding the holographic principle via RG flow

Cited by 11 publications

References 43 publications

Developing local RG: quantum RG and BFSS

Developing local RG: quantum RG and BFSS

Illustrated study of the semiholographic nonperturbative framework

A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

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